Carbon emission permit price volatility reduction through financial options

ENEECO-02799; No of Pages 13 Energy Economics xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Energy Economics journal homepage: www.elsevier.com/locate/eneco

Carbon emission permit price volatility reduction through financial options Li Xu a, Shi-Jie Deng a,⁎, Valerie M. Thomas a,b a b

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive NW, Atlanta, GA 30332, United States School of Public Policy, Georgia Institute of Technology, 685 Cherry Street, Atlanta, GA 30332, United States

a r t i c l e

i n f o

Article history: Received 29 September 2013 Received in revised form 3 June 2014 Accepted 8 June 2014 Available online xxxx JEL classifications: G12 G13 G23 Q51 Q56 Q58

a b s t r a c t We develop a stylized model to investigate the impact of financial options on reducing carbon permit price volatility under a cap-and-trade system. The existence of an option market provides a mechanism to hedge the uncertainty of future spot prices and is a stimulus for investment in carbon emission abatement technologies. We show that both the spot price level and the price volatility of carbon permits can be reduced via the trading of financial options, while achieving the emission reduction target. We also show that introducing financial options in a banking environment offers more flexibility to risk management in carbon permit trading. © 2014 Elsevier B.V. All rights reserved.

Keywords: Carbon permit trading Financial options Volatility mitigation Emission permit pricing

1. Introduction Cap-and-trade mechanisms are market-based approaches to control greenhouse gas pollution. Under the Kyoto Protocol, the European Union established a cap-and-trade system to reduce greenhouse gas emissions. In the U.S., similar mechanisms were introduced such as the Regional Greenhouse Gas Initiative (RGGI) in the ten eastern states, building on the cap-and-trade experience of the SO2 and NOx reduction policies (Napolitano et al. (2007)). Allowance trading rewards efficient energy production/consumption and motivates emission reduction. Thus, cap-and-trade programs provide flexibility to energy producers and consumers in designing their own compliance strategy while ensuring that the overall emission reduction targets are achieved, as discussed in Aldy et al. (2009), Stavins (2008), Tietenberg (2006), Bushnell and Chen (2009), Eshel (2005). Bertrand (2013) offered a comprehensive review of the cap-and-trade implementation of emission control. The concept of cap-and-trade was first introduced in Dales (1968). He showed that emission trading is able to achieve the emission reduction targets at the lowest social cost, when the marginal abatement cost is the same among all regulated polluters. Montgomery (1972)

⁎ Corresponding author. Tel.: +1 404 894 6519; fax: +1 404 894 2301. E-mail address: [email protected] (S.-J. Deng).

formalized this result. He proposed a static and deterministic model showing that there exists an equilibrium in a competitive permit market without transaction costs. Based upon this work, research on modeling the emission permit markets in dynamic and stochastic settings has been proposed. Tietenberg (1985) and Cronshaw and Kruse (1996) developed a discrete-time deterministic model with banking and borrowing allowed. In their models, the permit price rises at a rate equaling the interest rate. Rubin (1996) further extended the results to a continuoustime setting. Furthermore, he obtained that if borrowing is restricted, the growth rate of the marginal abatement cost and the permit price are less than the rate of interest. Schennach (2000) explored the consequences of constraints on borrowing. Random emissions were incorporated into modeling the permit price dynamics. The expected permit prices are shown to grow at the discount rate when the constraint on borrowing is not binding, while the expected prices rise at a rate less than the discount rate when the borrowing constraint is binding. The same results were proved in Newell's (2005) study under a stochastic model and it was further shown that the cap-and-trade system with banking and borrowing would be largely equivalent to an emission tax system. Given that the success of the permit markets critically depends on how well the markets meet the hedging needs, it is imperative to understand not only the path of the expected permit prices, but also the magnitude of price fluctuation around the expected price levels. Whether or

http://dx.doi.org/10.1016/j.eneco.2014.06.001 0140-9883/© 2014 Elsevier B.V. All rights reserved.

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

2

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

not the permit price volatility would be confined to a reasonable range is a key to the market design for an efficient and effective cap-and-trade program. The issue of permit price volatility has been investigated in the literature. For example, Celebi and Graves (2009) estimated a standard deviation of 50% or more for CO2 price per year in the U.S. under America's Climate Security Act proposed by Lieberman and Warner in 2007. As it is argued that a cap-and-trade market mechanism for carbon may offer stronger incentives for carbon reduction technology investment (e.g., Chen and Tseng (2011)), high volatility in CO2 price could discourage and delay investment in the CO2 abatement technologies needed to achieve large reductions in carbon emissions. We contribute to the body of knowledge on the design of mechanisms for reducing carbon permit price volatility by examining the role of trading permit options in influencing the permit price volatility and its implications on carbon emission reduction policy design. Specifically, we show that the trading of properly designed financial options on carbon permits can prevent excessive price volatility in the spot market for permits and reduce overall carbon emission reduction costs. Several approaches have been proposed to address the price volatility issue in carbon emission trading. Jacoby and Ellerman (2004) proposed a safety valve mechanism which includes a slowly evolving price floor and ceiling. They mentioned that this mechanism does reduce price volatility, however, a low price ceiling can lead to extra emissions. Kijima et al. (2010) showed that the emission permit price spikes, which are a major cause of price volatility, can be reduced by allowing permits to be banked. While the effects of banking of permits on smoothing permit prices and lowering costs are well studied in the literature, Fell et al. (2008) showed that the permit price volatility remains large with the persistence of baseline emission shocks. They suggested there may still be motivation for considering price mechanisms in addition to banking. Other authors also investigated the impact of bankable permits on permit price and price volatility reduction. Maeda (2004) studied the linkage between the spot price and the future price of bankable permits. He showed that an increase in the uncertainty in future prices would first lower the spot price and then cause an increase in spot price with the futures price volatility getting too high. He also studied how future spot volatility may affect the spot price level and the banking behavior. Empirically, Alberola and Chevallier (2009) showed that the low European Union Allowance (EUA) spot price during Phase I (2005– 2007) was partially due to the unlimited intra-phase banking and restricted inter-phase banking between Phase I and II. The intra-phase banking can increase the abatement and spot price in the early phase of a program, but can knock them down at the end of the same phase. Seifert et al. (2008) showed the price volatility in EU ETS increases when time approaches the end of the Phases, while, at the same time, the volatility decreases when the price is close to its bounds. Carmona et al. (2010) also showed that such phenomenon is a general result of cap-and-trade systems without inter-phase banking. Assuming that inter-phase banking is allowed, Hitzemann and Uhrig-Homburg (2010) found that the price of allowances and its volatility depend on upcoming Phases, and illustrated that each additional Phase leads to an additional component in the current price. Although these studies conclude that banking is able to stabilize the expected permit price level, price variability may remain large. How banking or other mechanisms may affect the future price volatility needs further study. It is well-known from the finance literature that, in a world with complete markets, symmetric information, and no transaction costs, the trading of financial options would have no effect on their underlying assets. However, as most financial markets including carbon permit markets are inherently incomplete and prone to asymmetric information, options can affect their underlying assets in various aspects. In a setting with incomplete markets and transaction costs, Grossman (1988) showed that the trading of options may indeed affect the price volatility of the underlying assets. In the financial equity markets, researchers find that the magnitude of reduction in the price volatility of the underlying assets following the introduction of their options' trading ranges from

4% to 20% (see, for instance, Conrad (1989), Bansal et al. (1989), Skinner (1989), Damadoran and Lim (1991)). In the commodity markets, for example, the crude oil market, Fleming and Ostdiek (1999) report that deep and liquid future markets may reduce the volatility of the underlying market. On the other hand, the introduction of crude oil options and other energy derivatives has little effect on increasing the price volatility, because they gradually complete the market. Carbon futures and options are actively traded in the European Emission Trading Scheme (EU ETS). European Union Allowance (EUA) and Certified Emission Reduction (CER) futures and options are also traded through exchanges including NYMEX, Nasdaq OMX, and ICE in the United States. Leconte and Pagano (2010) argued that in the European carbon market, insufficient market regulation drove the market to deviate from its critical functions of price discovery and risk transfer. To ensure a properly functioning derivative market, they as well as Grüll and Taschini (2011) suggested a range of regulatory actions, such as screening of market participants. In this paper, in the context of a properly functioning derivative market, we investigate the trading of financial options on CO2 permits as an alternative approach for carbon permit price volatility reduction. Chesney and Taschini (2008), Daskalakis et al. (2009), Hintermann (2013), Kijima et al. (2010), among others, have studied the pricing problems of options written on emission allowances in emission permit markets. A complete understanding on how to properly price the emission permit options facilitates the development of the corresponding options markets. Grüll and Taschini (2011) illustrated that popular price-risk hedging mechanisms, such as price floor, price collar and allowance reserve, can be replicated through plain European- and American-style permit options. This implies that emission permit options can be efficient and sufficient tools for managing permit price risks, and their results also hold when banking is allowed. Recently, Chevallier et al. (2011) completed an empirical study on the effect of the introduction of options on emission permit price volatility based on data collected from EU ETS. They suggested that the introduction of options may decrease the price volatility level of emission permits. However, they did not investigate the causes behind this effect in detail. Through a stylized model, this paper demonstrates that introducing a market for properly designed financial options on emission permits increases the price elasticity of permit demand. We find that the trading of such options reduces the inter-temporal variation of the spot price level, the price volatility of CO2 permits, and the total cost of achieving emission reduction targets. We also show that the financial option approach works more effectively in a system with banking than in a system without banking. In contrast to the priceceiling approach, the options approach does not result in extra emissions. Furthermore, the existence of option markets enable the regulated emitting sources to hedge the uncertainty of future emission permit prices and stimulates investment in carbon emission abatement technologies. The reminder of the paper is organized as follows. We formulate a two-compliance-time model of a carbon cap-and-trade system without inter-period banking or trading of financial instruments in Section 2. Then we analyze the effect of the following four approaches on the volatility of emission permit price: 1) safety valve, 2) banking/borrowing, 3) financial options, and 4) financial options in a bankable system in Section 3. We follow up with a numerical example for illustration. Finally, we conclude that the permit options mechanism is a promising approach for reducing both the emission permit price volatility and the cost of achieving emission reduction target.

2. A two-compliance-time model: the base case We consider a model in which there are only two compliance times, the present time (t = 0) and the future time (t = 1). Carbon permits are traded in a spot market at both times.

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

In this base case model, we assume that there are N regulated carbon-emitting sources (or, emitters) in the system1. For each emitter i (i = 1,⋯,N), the business-as-usual emission quantity at time t is denoted as ei,t, and the allocated emission allowances at time t are denoted as ai,t. We denote Pt as the spot price at time t and Ci,t = Ci,t(qi,t) as the cost function of reducing emission by an amount of qi,t for source i at time t. To focus on developing insights on volatility mitigation, we employ stylized cost model for emission reduction. Explicit cost models of emission reduction can be found in related literatures (see Carmona et al. (2010), Hintermann (2010)). We assume that the emission allowances are initially allocated freely. The business-as-usual emission quantity of emitter i at time 1, denoted by ei,1, is modeled by a random variable at time 0, which has a distribution over a probability space (Ω,F,P) with mean μi,1 and variance σ 2i,1. The randomness in emission quantities drives the uncertainty of the spot price P1 at time 0. Usually the business-as-usual emission quantities of different emitters, for example, power plants, are driven by some common factors, so we assume that ei,1 and ej,1 are correlated with each other with correlation coefficient ρij for any i, j = 1,⋯,N. We also impose a condition that a regulator always allocates less emission permits to the emitters than their expected business-as-usual emission quantities, i.e., ai,1 b μi,1, i = 1,⋯,N. This condition is natural given the policy goal of emission reduction and it ensures the positive expectation of emission permit prices. From the perspective of a regulator, the policy goal is to achieve the desired carbon emission reduction targets with the lowest costs to the regulated emitters during each compliance period. All regulated emitters would equate their respective marginal costs of emission reduction to the permit price, which results in the low marginal emission reduction cost emitters to increase their abatement levels relative to those of the high-cost emitters. The corresponding problem of the regulator in this base case is formulated as follows:

min qi;t

N X

  C i;t qi;t

i¼1

N N h i X X qi;t ¼ ei;t −ai;t ; t ¼ 0; 1: s:t: i¼1

ð1Þ

3

The spot price P1 is determined by imposing the following market clearing condition at time 1: N X

qi;1 ðωÞ ¼

i¼1

N h X

i ei;1 ðωÞ−ai;1 ; ω∈Ω:

Since everything at time 0 is known, the market clearing condition at time 0 is similarly written as: N X

qi;0 ¼

i¼1

N h X

i ei;0 −ai;0 :

ð4Þ

i¼1

By applying Eq. (2), we have the spot prices at time 0 and time 1 determined as: XN h P0 ¼

i¼1

ei;0 −ai;0

XN

c−1 i¼1 i;0

i

XN h ;

P 1 ðωÞ ¼

h i    TC i;1 ðωÞ ¼ P 1 ðωÞ ei;1 ðωÞ−qi;1 ðωÞ −ai;1 þ C i;1 qi;1 ðωÞ :

ð5Þ

ð7Þ

Fig. 1 illustrates the market equilibrium at time 1 in this case. In this figure, D1(ω) = ∑ N i = 1 [ei,1(ω) − ai,1] stands for the net demand of required emission reduction at time 1, which is random. S1 is the aggregate supply curve at time 1, which is equivalent to the aggregate N −1 marginal cost curve, ∑ N i = 1 qi,1(ω)/∑i = 1 ci,1 = P1(ω). The intersection of them determines the emission permit price at time 1, P1(ω), and the total actual emission reduction at time 1, Q1(ω). These notations are used in the subsequent figures. For simplicity, we consider that these N regulated emitters are symmetric, i.e., ei,1 are independent and identically distributed (i.i.d.). So we omit the subscript i in our notation and obtain the following expressions: P 0 ¼ c0 ðe0 −a0 Þ;

ð8Þ 2

E½P 1  ¼ c1 ðμ 1 −a1 Þ; Var ½P 1  ¼

 0  P 1 ðωÞ ¼ C i;1 qi;1 ðωÞ ; i ¼ 1; ⋯; N:

i ei;1 ðωÞ−ai;1 ; XN c−1 i¼1 i;1

i¼1

and the minimized total costs for meeting the emission-cap requirements of ai,0 and ai,1 are: h  i   ð6Þ TC i;0 ¼ P 0 ei;0 −qi;0 −ai;0 þ C i;0 qi;0 ;

i¼1

The solution to problem (1) yields the lowest social cost for achieving required emission reduction target. However, from the perspective of emitters, the goal is to minimize their individual costs. Specifically, at time 1, for any realized spot price P1(ω), ω ∈ Ω, each emitting source chooses its emission reduction quantity qi,1(ω) such that P1(ω) is equal to its marginal cost, i.e.

ð3Þ

i¼1

2

c1 σ 1 ; N

ð9Þ

" # 1 c0 ðe0 −a0 Þ2 1 c1 ðμ 1 −a1 Þ2 c1 σ 21 TC ¼ TC 0 þ þ þ : E½TC 1  ¼ 2 2 2N 1þr 1þr ð10Þ

ð2Þ

Here, each emitting source is assumed to be a price taker. If each emitter acts in this way, the outcome is equivalent to the first-best solution in problem (1). For simplicity,   we assume that the cost function of each emitter is quadratic: C i;t qi;t ¼ 12ci;t q2i;t , i = 1,⋯,N, where ci,t N 0 represents the growth rate for the marginal cost of emission reduction as the reduction quantity increases. The economic efficiency of the emission reduction technology of emitter i in reducing emission at time t is proxied by ci,t, for instance, the smaller the ci,t, the higher the technological efficiency. 1 In later sections, we extend this model to include unregulated sources which play a role of supplying financial options. In the base case model, there are no banking and no financial instruments involved.

Fig. 1. Market equilibrium in the base case.

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

4

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

We find that the variance of emission permit prices or the price volatility decreases as the number of emitters, N, increases. This means the uncertainty in business-as-usual emission quantities and the spot prices can be offset as N increases due to the law of large numbers. The quantity dTC/dc1 is given by: " # dTC 1 ðμ 1 −a1 Þ2 σ 21 þ N0: ¼ 2 2N dc1 1 þ r

ð11Þ

dTC/dc1 measures the change of an emitter's total cost for achieving emission target per unit change in the growth rate c1 of its marginal emission reduction cost. Eq. (11) implies that every unit of decrease in the growth rate of the marginal cost for emission reduction would definitely lead to reduced total cost for an emitter to achieve the emission reduction target. As c1 is inversely related to the economic efficiency of emission reduction technology, investment in enhancing the emission abatement technology would generally result in a decreased level of c1. dTC/dc1 is therefore used as a measure for the incentive to invest in emission reduction technology by a regulated emitter. If the investment cost for enhancing the economic efficiency of current emission reduction technology (namely, lowering c1) is less than dTC/dc1, then regulated emitters would have an incentive to invest in emission reduction technology. In the subsequent sections, the above expressions are used as benchmarks for contrasting the effects of different volatility reduction approaches. We summarize the expressions in Table 3 at the end of Section 4 to facilitate the comparison.

Setting safety valves does reduce the variance or the volatility of the spot price, while the change of the expected price depends on the choice of the floor P and the ceiling P. However, if a price ceiling is imposed, an imbalance between supply and demand may occur. In a carbon emission market, when the spot price is higher than P, the regulator needs to issue new allowances of carbon emissions to buyers at the price ceiling to fill in for the supply shortage, resulting in emissions above the policy target. Fig. 2 illustrates the market equilibrium at time 1 in the safety valve case. When the price ceiling P is lower than the equilibrium price, the supply curve determines the corresponding total emission reduction Q 1 . The difference between Q 1 and Q1(ω) is shown as the shortage. 3.2. Banking and borrowing approach The second approach we discuss is a banking and borrowing mechanism. When banking is allowed, the regulated emitters are able to save their unused allowances for use in the future compliance period, or even purchase allowances from the current spot market and hold them to hedge against high permit price scenarios in the future. When borrowing is allowed, the emitters can use the future allowances to cover a shortage in the current period, or even sell them in the current spot market to hedge against scenarios of declining permit price in the future. A linkage between the current price of permits and their prices in the future is therefore established. In our two-compliance-time model, each emitter i can bank or borrow allowances Bi,0 at time 0. Bi,0 N 0 and Bi,0 b 0 correspond to banking and borrowing, respectively. Then the market clearing conditions at time 0 and time 1 are:

3. Price volatility reduction via different approaches

N X

In this section, we study different approaches to permit price volatility reduction in the framework of the above two-compliance-time model. We analyze the following four schemes: 1) safety valve, 2) banking/ borrowing, 3) financial options, and 4) financial options in a bankable system, and we also compare their performance.

i¼1

N h X

i ei;0 −ai;0 þ Bi;0 ;

ð12Þ

i¼1

N X

qi;1 ðωÞ ¼

i¼1

3.1. A safety valve approach First, we look at the safety valve approach. A safety valve refers to a price limit for confining the spot price of emission permits to a desired range. With this approach, a regulator puts a floor P and a ceiling P on the spot price. When the spot price exceeds the price ceiling, market buyers can purchase permits from the government at this regulated ceiling. When the spot price falls below the price floor, market sellers can sell permits to the government at this floor. In this case, the spot price at time 1 is P v1 ðωÞ ¼ P∨P 1 ðωÞ∧P.

qi;0 ¼

N h X

i ei;1 ðωÞ−ai;1 −Bi;0 ; ω∈Ω:

By Eq. (2), the spot prices at time 0 and time 1 are obtained: XN h b P0

¼

i¼1

i ei;0 −ai;0 þ Bi;0 ; XN c−1 i¼1 i;0

b P 1 ðωÞ

i XN h ei;1 ðωÞ−ai;1 −Bi;0 i¼1 ¼ : XN c−1 i¼1 i;1 ð14Þ

The total costs of achieving ai,0 and ai,1 are b

b

TC i;0 ¼ P 0

h  i   ei;0 −qi;0 −ai;0 þ Bi;0 þ C i;0 qi;0 ;

h i    b b TC i;1 ðωÞ ¼ P 1 ðωÞ ei;1 ðωÞ−qi;1 ðωÞ −ai;1 −Bi;0 þ C i;1 qi;1 ðωÞ :

P b0

Fig. 2. Market equilibrium in the safety valve case.

ð13Þ

i¼1

ð15Þ

ð16Þ

Comparing Eq. (14) with Eq. (5), we note that, if ∑ N i = 1 Bi,0 N 0, then h i b b N P0 and E P 1 bE½P 1  but Var[P 1] does not change. This implies that

bankable permits are able to stabilize the spot price process in the sense that they make the expected difference between the future permit price and the current price smaller than the expected price difference in the base case. However, the variance (or, volatility) of the permit price at time 1 remains at the same level as that in the base case. The left panel of Fig. 3 plots the market equilibrium at time 0 in the banking case. It shows that positive net banking B = ∑ N i = 1 Bi,0 increases the demand for emission reduction from D0 to Db0, and consequently raises the price level at time 0. The right panel of Fig. 3 plots the market equilibrium at time 1. It shows that positive net banking B decreases the demand for emission reduction from D1(ω) to Db1(ω) at

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

5

Fig. 3. Market equilibrium in the banking case at time 0 (left) and at time 1 (right).

time 1, which shifts the demand curve towards the left. This parallel shift of demand curve leads to the decrease in the expected equilibrium price while keeping the variance of the price unchanged. We also note in Fig. 3 that the price difference between time 0 and time 1 with banking (ΔP b) is smaller than that in the case without banking (ΔP). In order to determine the optimal quantity of permit banking/ borrowing B∗i,0, we assume that each emitter i aims at minimizing its own total expected discounted cost of emission reduction: b

b

TC i ¼ TC i;0 þ

h i 1 b E TC i;1 ; i ¼ 1; ⋯; N; 1þr

 X h i i XN h N ei;0 −ai;0 þ Bi;0 þ ei;0 −ai;0 þ Bi;0 ei;0 −ai;0 þ Bi;0 i¼1 i¼1 −1 −ci;0 XN X 2 N c−1 c−1 i¼1 i;0 2



XN h

i

i¼1 i;0

μ i;1 −ai;1 −Bi;0 1 6 μ i;1 −ai;1 −Bi;0 þ i¼1 −1 − −ci;1 XN 4 −1 1þr c i;1 i¼1 ¼ 0:

i3 μ i;1 −ai;1 −Bi;0 7 X 2 5 N c−1 i¼1 i;1

XN h i¼1

ð18Þ

∗ By summing up Eq. (18) in i from 1 to N, we solve for ∑ N i = 1 Bi,0:

N X i¼1

XN   Bi;0

¼

i¼1

 X  X XN  N N μ i;1 −ai;1 = i¼1 c−1 ei;0 −ai;0 = i¼1 c−1 i;1 −ð1 þ r Þ i;0 i¼1 : XN XN −1 ð1 þ r Þ= i¼1 c−1 þ 1= c i;0 i¼1 i;1

ð19Þ The Cournot–Nash equilibrium (B∗1,0,B∗2,0,⋯,B∗N,0) are obtained by plugging Eq. (19) into best response functions (Eq. (18)). To further understand the implications of a banking mechanism, we consider the simplified symmetric case as described in the base case. We obtain the following: b P0

¼ c0 ðe0 −a0 þ B0 Þ;

h i h i c2 σ 2 b b E P 1 ¼ c1 ðμ 1 −a1 −B0 Þ; Var P 1 ¼ 1 1 : N

time 0 stabilizes the spot price process as explained under the general setting. The total discounted cost in Eq. (17) is simplified as: b

b

TC ¼ TC 0 þ

ð17Þ

where r is the interest rate, and that all emitters make decisions independently and simultaneously. This presents a game with N players whose strategic decisions over the amount of Bi,0 form a Cournot–Nash equilibrium. To find the equilibrium, we first solve the best response functions of these players from the first-order condition of Eq. (17). We have the following for each i, i = 1,⋯,N, 

Comparing Eqs. (20) and (21) with Eqs. (8) and (9), we note that P b0 N h i P0 and E P b1 bE½P 1  when B0 N 0, which means that banking permits at

¼

h i 1 b E TC 1 1þr

" # c0 ðe0 −a0 þ B0 Þ2 1 c1 ðμ 1 −a1 −B0 Þ2 c1 σ 21 þ þ ; 2 2 2N 1þr

ð22Þ

where r is the interest rate. We also simplify Eqs. (18) and (19) to get the explicit form of the optimal banking quantity B∗0 for each emitter, 

B0 ¼

c1 ðμ 1 −a1 Þ−c0 ð1 þ r Þðe0 −a0 Þ : c0 ð1 þ r Þ þ c1

ð23Þ

Eq. (23) yields the following condition under which an emitter would save a positive quantity of emission permits at time 0 for use at time 1: c1 ðμ 1 −a1 Þ Nc0 ðe0 −a0 Þ: ð1 þ rÞ

ð24Þ

Namely, B∗0 N 0 if condition (24) holds. This means that an emitter would save a positive amount of emission permits at time 0 if the present value of the marginal cost for reducing 1 unit of emission at the expected emission reduction target level (μ1 − a1) at time 1 is greater than that for reducing 1 unit of emission at the time-0 emission reduction target level (e0 − a0). The effect of improvement in the economic efficiency of current emission reduction technology on the total discounted emission reduction cost, dTCb ∗/dc1, is given by: " # b  2 2 dTC 1 ðμ 1 −a1 −B0 Þ σ1 þ N0: ¼ dc1 2 2N 1þr

ð25Þ

ð20Þ

This shows that, by improving the economic efficiency of emission reduction technology, one would definitely reduce the total discounted cost of achieving the emission reduction target. Comparing dTCb ∗/dc1 with dTC/dc1 in Eq. (11), we get,

ð21Þ

dTC dTC b dc1 dc1

b

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

6

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

if regulated emitters choose to bank a positive amount of permits at time 0 (namely, B∗0 N 0). This implies that, when it is optimal for the regulated emitters to bank emission permits at time 0, they would have less incentive to invest in enhancing the emission abatement technology in the banking case than they do in the base case. This is because, in the base case, investing to improve the economic efficiency of emission abatement technology is the only means to reduce the total discounted cost for an emitter, while in the banking case, the bankable permits substitute the investment for improving emission reduction technology in getting the cost-reduction benefits. On the benefits of the banking approach, as the bank permits get used in the second compliance period, there is no need for issuing extra emission allowances to meet the emission reduction target over the two-compliance-period. Furthermore, as the total discounted emission reduction cost in the base case is achievable in the banking case by setting B0 = 0, the optimized cost of achieving emission reduction target in the banking case shall be less than that in the base case, namely, TCb ∗ b TC. Finally, we plug B∗0 into Eqs. (20) and (21), and obtain:

b

P0 ¼

c0 c1 ðe0 −a0 þ μ 1 −a1 Þ c0 ð1 þ r Þ þ c1

h i c c ð1 þ r Þðe −a þ μ −a Þ b b 0 0 1 1 E P1 ¼ 0 1 ¼ ð1 þ r ÞP 0 : c0 ð1 þ r Þ þ c1

ð26Þ

ð27Þ

This means that, following the optimal strategy of banking/borrowing emission permits, the expected permit price rises at the interest rate, which is consistent with the result of Newell (2005). We summarize the findings in the following propositions. Proposition 1. Banking only For symmetric regulated emitters, if the present value of the marginal cost for reducing 1 unit of emission at the expected emission reduction target level (μ1 − a1) at time 1 is greater than that for reducing 1 unit of emission at the time-0 emission reduction target level (e0 − a0), namely, c1 ðμ 1 −a1 Þ Nc0 ðe0 −a0 Þ ð1 þ r Þ then the emitter bank permits at time 0 for future usage, equivalently, the optimal banking/borrowing quantity B∗0 is positive. This stabilizes the spot price process with the price volatility unchanged. Remark. If the marginal cost of emission reduction is non-linear, for instance, a general convex function, in emission reduction quantity, the banking approach may reduce the price volatility as well. Proposition 2. Banking only For symmetric regulated emitters, if c1 ðμ 1 −a1 Þ Nc0 ðe0 −a0 Þ; ð1 þ r Þ then the change of total discounted cost with respect to the change in the growth rate of the marginal emission reduction cost in the banking case is less than that in the base case, namely,

3.3. Financial options approach In this section, we investigate a financial options approach for reducing carbon emission permit price volatility. Under the same setting as the base case model, we introduce a class of innovative financial options whose underlyings are emissions permits; we demonstrate that the trading of such options helps improve the efficiency of the emission permit market in many aspects. In the financial equity markets, researchers argue that there are several reasons why volatility reduction in a stock price return is expected to occur after the introduction of trading of derivatives on the stock. In the context of futures contracts, Stein (1987) showed that volatility reduction can be achieved when the benefit of risk sharing by the derivative securities outweighs the possible volatility-increasing effect due to speculative trading. For options markets, both improved risk-sharing (in the case of options extending the hedging contingency set) and the lowered transaction costs (due to leverage offered by options) attract more informed trading activities in the options markets, making the underlying price reflect more information about the underlying assets Cao (1999). This improves information sharing and reduces the risk of investing in the underlying assets, and in turn tends to raise the underlying asset prices and make them less volatile Conrad (1989) and Roll et al. (2009). A call option on a carbon emission permit gives the holder the right but not the obligation to purchase the underlying permit at the predetermined strike price at a pre-specified maturity time. Call options offer buyers a means of hedging the risk of high future permit prices. We assume that call options on emission permits delivered at time 1 at all strike prices are traded and there exist M unregulated firms participating in the emission permit options markets. These unregulated sources for emission permits could be companies which provide carbon emission offsets that meet verification requirements of the regulators, thus assuming the role of sellers of the emission options. The regulated emitters would be the natural buyers of the emission options. There may also exist speculators who take on the roles of buyers and/or sellers in the emission options trading due to splitting opinions on the future underlying price. We consider a new class of financial options written on emission permits with maturity time 1, termed as the emission permit option bundles. • An emission permit option bundle is an option instrument written on carbon emission permits which has a time-1 payoff given by that of a portfolio of standard call options on emission permits with strike price K spanning all possible permit price levels (for instance, the strike prices can be uniformly distributed from zero to a large price cap). The density distribution of the shares of the call options in the bundle over all strike prices is uniformally 1. We refer to it as an option bundle, or a bundle, from here on. Chao and Wilson (2004) discuss the use of such option bundles written on electricity in the electricity reserve capacity markets. At time 0, these option bundles are traded among the regulated emitters and the unregulated sources for delivery of emission permits (or, the corresponding financial settlements) at time 1. After a market participant purchases a bundle at time 0, the permit price realizes to be P1 at time 1 and the participant exercises all the call options with strike price K ranging from 0 to P1. The higher the P1, the more call options would get exercised by the holder at time 1, that is, the number of permits settled via option-exercise at time 1 are positively correlated with the permit price P1. As the density of the shares of the call option at each strike price level is 1, the number of permits delivered through exercising call options

dTC b dTC b ; dc1 dc1

equals ∫0 1dK ¼ P 1 at time 1 for 1 unit of the bundle, and the payoff

and the total discounted cost of achieving required emission reduction in the banking case is always less than that in the base case, TCb ∗ b TC.

Let θi and γj denote the number of bundles purchased or sold by the regulated emitter i and the unregulated source j, respectively, where

P1

P1

of this bundle is ∫0 maxðP 1 −K; 0ÞdK ¼ 12P 21 .

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

i = 1,⋯,N and j = 1,⋯,M. A positive (or, negative) number of shares correspond to a buy (or, sell) transaction. The price of such a bundle is denoted by λ. As these option bundles offer their buyers a means to hedge the risk of high permit prices at time 1, the regulated emitters act as the natural buyers of the bundles. When the permit price P1 gets realized at time 1, a portfolio of θi units of the option bundles offer its holder the right to acquire θiP1 shares of permits for a cost of 12θi P 21 as opposed to θiP 21 if purchasing the θiP1 shares in the spot market directly. On the selling-side of the market, the unregulated sources act as the natural sellers of the option bundles. For example, companies with carbon reducing capabilities can earn emission permits by reducing greenhouse gas emissions and then sell option bundles against the earned permits. The received options premiums compensate for the investment in the research and development of the emission reduction technologies. We assume that each unregulated source j, namely, firm j, has its own cost structure for carbon abatement. Specifically, the cost of firm j sequestering or storing q units of gas emission is assumed to be a quadratic function 12h j q2 where h j ( j = 1,⋯,M) is a firm-specific constant parameter. With the ability to earn emission permits, the unregulated sources do not need to buy permits from the spot market at price P1 to meet the delivery requirements of the exercising of option bundles. Instead, they use their facilities to reduce carbon emissions and deliver the earned permits. The condition for firm j to act as a seller of the option bundles is given below: 2 1 1  2 − γ j P 1 ≥ h j γ j P 1 ; j ¼ 1; ⋯; M: 2 2

ð28Þ

This means that the revenue received from the strike prices for delivering − γjP1 units of emission permits to the option bundle buyer is sufficient to cover the cost of earning the permits. An upper bound for the shares of option bundles sold by firm j is obtained from Eq. (28): 0≤−γ j ≤ h1 , j = 1,⋯,M. As γj denotes the shares of option bundles sold by the unregulated source j, it is negative by definition. Under the stylized quadratic cost function for carbon sequestering, there would be ample sellers of the option bundles to clear the option bundles market provided hj is sufficiently low. The market clearing conditions for the trading of permits and option bundles at time 0 are: j

N X i¼1

qi;0 ¼

N h X i¼1

N M i X X ei;0 −ai;0 ; θi ¼ − γ j: i¼1

ð29Þ

j¼1

The market clearing condition for setting the permit price P o1(ω) when the state of the world ω occurs at time 1 is (the superscript “o”

7

in P o1(⋅) stands for the “financial option” case): N h X

N h i X i o qi;1 ðωÞ þ θi P 1 ðωÞ ¼ ei;1 ðωÞ−ai;1 ; ω∈Ω:

i¼1

ð30Þ

i¼1

By applying Eq. (2), we get the respective permit prices at time 0 and time 1 to be: XN h o P0

¼

i¼1

ei;0 −ai;0

XN

c−1 i¼1 i;0

i

XN h ;

o P 1 ðωÞ

¼

ei;1 ðωÞ−ai;1 i¼1 i XN h c−1 i;1 þ θi i¼1

i :

ð31Þ

The total cost of achieving emission targets (i.e., caps) ai,0 and ai,1 are o

o

TC i;0 ¼ P 0

h  i   ei;0 −qi;0 −ai;0 þ λθi þ C i;0 qi;0 ;

o

o

TC i;1 ðωÞ ¼ P 1 ðωÞ

h

ð32Þ

i 1     2 o ei;1 ðωÞ−qi;1 ðωÞ −ai;1 − θi P 1 ðωÞ þ C i;1 qi;1 ðωÞ : 2 ð33Þ

Comparing Eq. (31) with Eq. (5), we note that, if ∑ N i = 1 θi N 0, then   P o0 = P0, E P o1 bE½P 1  and Var[P o1] b Var[P1]. This implies that a positive net purchase of option bundles by the regulated emitters simultaneously reduce the expected price level and the price volatility of the emission permits traded at time 1 from their respective levels in the base case. The left panel in Fig. 4 plots the market equilibrium at time 1 in the financial option case. It shows that the positive net purchase of option bundles Θ = ∑ N i = 1 θi tilts the demand curve from its base case form D1(ω) to Do1(ω), i.e., increases the price elasticity of demand. The angle of tilting is tan−1Θ and it corresponds to ΘP o1(ω) shares of emission permits settled via the exercising of option bundles. This non-parallel shift of demand curve results in the reduction in both the expected equilibrium price and the price volatility from the base case levels. Assuming that each regulated emitter i aims at minimizing its own total expected discounted cost to meet emission-cap requirement by purchasing θi shares of option bundles, and the N regulated emitters make decisions independently and simultaneously; this again falls into a game setting where the strategic decisions of the N emitters form a Cournot–Nash equilibrium. We derive the optimal purchasing quantities of the option bundles θ∗i through solving for the Cournot– Nash equilibrium. Let TC oi denote the total cost of emitter i where the superscript “o” stands for the “financial option” case: o

o

TC i ¼ TC i;0 þ

h i 1 o E TC i;1 ; i ¼ 1; ⋯; N; 1þr

ð34Þ

Fig. 4. Market equilibrium in the financial option case (left) and the combined case (right).

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

8

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

where r is the interest rate. To find the equilibrium of this game, we first solve for the best response functions of the players from the first-order condition of Eq. (34). With the no-arbitrage condition imposed on the price of an option bundle, λ becomes a function of θi, i = 1,⋯,N. Specifically, λ ¼ λðθ1 ; ⋯; θN Þ ¼

 1 1  o 2 E P1 ; 1þr 2

ð35Þ

which is the discounted expectation of the option bundle's payoff at time 1. By setting the price of an option bundle to its discounted expected future payoff to prevent arbitrage, the two terms λθi and h   i o 2 1 1 in Eq. (34) get canceled with each other. 1þr E 2θi P 1 From the first order condition of Eq. (34), the following holds true for regulated emitter i, i = 1,⋯,N  X   X N 2 μ i;1 −ai;1 μ i;1 −ai;1 þ σ i;1 þ ρ σ σ j≠i ij i;1 j;1 i¼1 − hX  i2 N c−1 i;1 þ θi i¼1

hX   i2 X XN X N N −1 2 ci;1 μ −a þ σ þ ρ σ σ i;1 i;1 ij i;1 j;1 i;1 j≠i i¼1 i¼1 i¼1 þ hX  i3 N −1 ci;1 þ θi i¼1 ¼ 0:

implemented, it is easy to verify that the discounted expectation of payoff of an option bundle is equal to its exogenous price λ:  1 1 o2 E P 1 ≡ λ; 1þr 2

ð39Þ

which implies that the equilibrium strategy consisting of θ∗i 's for the regulated emitters still ensures no-arbitrage in the option bundles market. The chosen θ∗i guarantees a partial equilibrium in the option bundles market. To clear the option bundles market, ∑ M j = 1γj needs to equal − ∗ ∑N i = 1 θi . This implies that to ensure price and volatility reduction from their respective base case levels, ∑ M j = 1 γj has to be negative, namely, the unregulated sources in the aggregate act as the net sellers of the option bundles. For the ease of discussion, we again consider the symmetric case as described in the base case to study the implications of the trading of option bundles. Under the symmetry assumption, Eq. (31) gets simplified and yields: o

P 0 ¼ c0 ðe0 −a0 Þ;

ð40Þ

 o  μ 1 −a1  o σ 21 E P 1 ¼ −1 ; Var P 1 ¼  2 : −1 c1 þ θ N c1 þ θ

ð41Þ

ð36Þ ∗ By summing up Eq. (36) over i from 1 to N, we obtain ∑ N i = 1 θi = 0. This means that if arbitrage opportunities are ruled out in the option bundles market, the aggregate purchase or sales of option bundles by the regulated emitters is zero. However, if λ is assumed to be an exogenous parameter,2 then the participants in the option bundles market are price-takers trading option bundles at a constant price λ per share. Discussion of pricing option contracts on tradable permits can be found in the studies of Daskalakis et al. (2009) and Kijima et al. (2010). In the case of option bundle price being exogenously set, we show that the equilibrium solution of θi would still ensure the no-arbitrage condition holding in the option bundles market. From the first order condition of Eq. (34), we have the following for each emitter i (i = 1,⋯,N):

½

 X   X N 2 μ i;1 −ai;1 μ i;1 −ai;1 þ σ i;1 þ ρ σ σ 1 i¼1 j≠i ij i;1 j;1 λþ − hX  i2 N 1þr c−1 i;1 þ θi hX  i2 X i¼1 XN X N N 2 μ i;1 −ai;1 þ σ þ ρ σ σ 1 i¼1 i¼1 i;1 i¼1 j≠i ij i;1 j;1 − hX  i2 N 2 −1 c þθ i¼1

þ



−1 ci;1

¼ 0:

þ θi



i;1

Comparing Eqs. (40) and (41) with Eqs. (8) and (9), we note that   E P o1 bE½P 1  and Var[P o1] b Var[P1] when θ N 0, which means that, net purchasing of option bundles by the regulated emitters simultaneously reduces the expected price level and the variance or volatility of permit price at time 1 from their respective base case levels, as explained under the general setting. The total discounted cost in Eq. (34) is simplified to: o

o

TC ¼ TC 0 þ

 o  c ðe −a0 Þ2 1 1 Nðμ 1 −a1 Þ2 þ σ 21   ; þ λθ þ E TC 1 ¼ 0 0 2 1þr 1 þ r 2N c−1 1 þθ ð42Þ

where r is the interest rate. We also simplify Eqs. (37) and (38) to get the explicit form of the optimal shares of bundles, θ∗, to purchase for each emitter, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Nðμ 1 −a1 Þ2 þ σ 21 −1 θ ¼ −c1 : 2Nλð1 þ r Þ 

i

hX  i2 X XN X N N 2 μ i;1 −ai;1 þ σ ρ σ σ i¼1 i¼1 i;1 i¼1 j≠i ij i;1 j;1 hX  i3 N c−1 i;1 þ θi i¼1



Eq. (43) yields the following condition under which a regulated emitter would be a buyer of option bundles at time 0 and exercise the bundles at time 1: λb

ð37Þ ∗ By summing up Eq. (37) over i from 1 to N, ∑ N i = 1 θi is expressed as:

vhffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i2 X XN X u XN  N 2 u N N μ i;1 −ai;1 þ σ þ ρ σ σ X X t i¼1 i¼1 i;1 i¼1  j≠i ij i;1 j;1 −1 θi ¼ − ci;1 : 2λ ð 1 þ r Þ i¼1 i¼1

ð38Þ The Cournot–Nash equilibrium (θ∗1,θ∗2,⋯,θ∗N) is obtained by plugging Eq. (38) into the best response functions (37). If (θ∗1,θ∗2,⋯,θ∗N) are

2 One justification for this assumption is that these option bundles cannot be exactly replicated by trading existing emission permits. The introduction of such option bundles indeed makes the markets more complete.

ð43Þ

" # 2 2 c1 c1 ðμ 1 −a1 Þ c σ þ 1 1 1þr 2 2N c1 E½TC 1  ¼ ; 1þr

ð44Þ

or μ 1 −a1 N

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2λð1 þ r Þ−Var ½P 1  : c1

ð45Þ

Namely, θ∗ N 0 if condition (44) or (45) holds. Condition (45) implies that regulated emitters become the buyers of option bundles if the regulator imposes a sufficiently tight cap a1 for time 1 such that the expected emission reduction target level μ1 − a1 at time 1 is greater than the lower bound specified in the right-hand side of Eq. (45). In other words, as long as the exogenous price of the option bundle λ is bounded by the scaled expected-cost of emission reduction at time 1 of the base case (namely, Eq. (44) holds), regulated

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

emitters become the buyers of the option bundles, while the unregulated sources are the sellers. Consequently, the trading of option bundles reduces both the expected price and the price volatility from their respective levels in the base case. In addition, we investigate the effect of improving the economic efficiency of current emission reduction technology on the total discounted emission reduction cost in the option case. This effect is captured by the quantity of dTC o ∗/dc1. N 0, Under the financial options approach, dTC o ∗/dc1 = λc−2 1 meaning that by improving the economic efficiency of emission reduction technology (namely, decreasing c1), one would definitely reduce the total discounted cost of achieving the emission reduction target, TC o ∗. When comparing dTC o ∗/dc1 with dTC/dc1 in Eq. (11), we note that, if the regulated emitters are net buyers of the bundles at time 0 (θ∗ N 0), then o

dTC =dc1 bdTC=dc1 : This implies that, when it is optimal for the regulated emitters to buy option bundles at time 0, they would have less incentive to invest in enhancing the emission abatement technology than they do in the base case. This is because unlike in the base case, where improving the economic efficiency of emission abatement technology is the only way for an emitter to reduce the total discounted emission reduction cost, in the case with option bundles, regulated emitters partially hedge the uncertainties in high emission reduction costs through purchasing bundles at time 0. The option bundles protect emitters from the high permit prices, thus substitute the investment for improving emission reduction technology in getting cost-reduction benefits. However, the emission permits that are settled from option bundles are created by unregulated sources. As the sellers of the option bundles, unregulated sources naturally have incentives to invest in enhancing the emission reduction technologies thus reducing the cost of delivering emission permits to the options buyers. Through the trading of option bundles, incentives for investing in emission abatement technology get reallocated between the emitters and the unregulated sources, namely, partially transferred from the regulated emitters to the unregulated sources. For the entire society, the overall investment incentives in enhancing the emission abatement technology would be preserved. If the price of the option bundle λ is greater than the scaled expected-cost of emission reduction at time 1 of the banking case (namely, condition (46) holds),

λN

h i c1 E TC b 1 1þr

ð46Þ

then we have dTC o ∗/dc1 N dTC b ∗/dc1, which implies that the regulated emitters would have stronger incentive to invest in improving emission abatement technology under the financial options approach than they do under the banking approach. On the benefits of the financial options approach, as the emission permits delivered through the exercising of option bundles are created by the unregulated sources, there is no need for the regulator to issue extra emission allowances to meet the emission reduction target over the two-compliance-period. Furthermore, as the total discounted emission reduction cost in the base case is achievable under the financial options approach by setting θ∗ = 0, the optimized cost of achieving emission reduction target in the option case shall be less than that in the base case, namely, TCo ∗ b TC. Of course, the introduction of such markets for the option bundles requires additional regulations and monitoring efforts. These regulatory costs, the operational costs and the transaction costs should also be taken into account when evaluating the overall benefits of the financial options approach.

9

Finally, the expected permit price and the variance of the permit price under the financial options approach are obtained by plugging θ∗ into Eq. (41):  o  E P1 ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  o  2Nλð1 þ r Þðμ 1 −a1 Þ2 2λð1 þ r Þσ 21 : ¼ ; Var P 1 Nðμ 1 −a1 Þ2 þ σ 21 Nðμ 1 −a1 Þ2 þ σ 21

ð47Þ

We summarize the above findings in the following propositions. Proposition 3. Options only Assuming all regulated emitters are symmetric, if the regulator imposes a sufficiently tight cap a1 for time 1 such that the expected emission reduction target level μ1 − a1 at time 1 is greater than the lower bound below μ 1 −a1 N

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2λð1 þ r Þ−Var ½P 1  ; c1

then the regulated emitters would purchase financial options at time 0, namely, the optimal quantity of option bundles purchased by an emitter, θ∗, is positive. The purchased option bundles reduce both the expected permit price and the permit price volatility from their respective levels in the base case. Remark. If the marginal cost of emission reduction is not linear, but a general convex function, bankable permits may reduce the permit price volatility but the option bundles would reduce the price volatility even more. Proposition 4. Options only Assuming that all regulated emitters are symmetric, the optimal quantity of option bundles purchased by an emitter, θ∗, which minimizes the total discounted emissionhreduction  2 i costs, ensures that the price of the op1 E 12 P o1 , namely, there is no arbitrage in the option bundle λ equals 1þr tion bundles market. Proposition 5. Options only Assuming all regulated emitters are symmetric, if h i c1 E TC b 1 1þr

bλb

c1 E½TC 1  ; 1þr

then the change of total discounted cost with respect to the change in the growth rate of the marginal emission-reduction cost in the option case is less than that in the base case but greater than that in the banking case, namely, b

o

dTC =dc1 bdTC =dc1 bdTC=dc1 : The total discounted cost of achieving required emission reduction in the option case is always less than that in the base case, TC o ∗ b TC. 3.4. Financial options in a bankable system From the analysis in the previous sections, we conclude that both banking and financial options are capable of reducing price volatility in carbon permit markets. They also reduce the total discounted cost of achieving the emission target without extra emission allowances issued over an entire control period. Due to the popularity of incorporating bankable permits in the recent cap-and-trade proposals, we are interested in studying the impact of introducing financial options on price volatility when emission permits are bankable. Under the framework described in the previous sections, we still consider only two compliance times 0 and 1. Each regulated emitter i can bank or borrow emission permits and trade option bundles on permits

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

10

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

at time 0. The same notations are used in this two-compliance-time model with both financial options and bankable permits. The market clearing conditions for the permits and the option bundles at time 0 are written as: N N h N M i X X X X qi;0 ¼ ei;0 −ai;0 þ Bi;0 ; θi ¼ − γ j : i¼1

i¼1

i¼1

i¼1

ob

ð48Þ

j¼1

N h i X i ob qi;1 ðωÞ þ θi P 1 ðωÞ ¼ ei;1 ðωÞ−ai;1 −Bi;0 ; ω∈Ω:

TC

ob

¼ TC 0 þ ¼

h i 1 ob E TC 1 1þr

c0 ðe0 −a0 þ B0 Þ2 1 Nðμ 1 −a1 −B0 Þ2 þ σ 21   þ λθ þ ; 2 1þr 2N c−1 1 þθ

ð55Þ

where r is the interest rate. The optimal amount of banking B∗0 and the shares of option bundles purchased, θ∗, for each emitter are determined by solving the following system of equations:

The market clearing condition for permits at time 1 is: N h X

The total discounted cost is simplified to be:

ð49Þ

c0 ðe0 −a0 þ B0 Þ−

i¼1

1 μ 1 −a1 −B0 ¼ 0; 1 þ r c−1 1 þθ

ð56Þ

and By Eq. (2), the equilibrium prices of permits at time 0 and time 1 are: XN h ob P0

¼

i¼1

ei;0 −ai;0 þ Bi;0 XN c−1 i¼1 i;0

i

i XN h ei;1 ðωÞ−ai;1 −Bi;0 ob i¼1 i :ð50Þ ; P 1 ðωÞ ¼ XN h −1 c þ θ i i;1 i¼1

The total cost of achieving ai,0 and ai,1 are: ob

ob

TC i;0 ¼ P 0

h

 i   ei;0 −qi;0 −ai;0 þ Bi;0 þ λθi þ C i;0 qi;0 ;

 h i 1 ob ob ob2 TC i;1 ðωÞ ¼ P 1 ðωÞ ei;1 ðωÞ−qi;1 ðωÞ −ai;1 −Bi;0 − θi P 1 ðωÞ 2   þ C i;1 qi;1 ðωÞ :

ð51Þ

ð52Þ

The right panel of Fig. 4 plots the market equilibrium at time 1 in this combined case. It shows that the positive net banking B shifts the demand curve D1(ω) towards the left, and at the same time, the positive net purchasing quantity of option bundles, Θ, tilts the demand curve to Dob 1 (ω), i.e., increases the price elasticity of demand. The angle of tilting is tan−1Θ and it corresponds to ΘP ob 1 (ω) shares of emission permits settled via options exercising. This movement also results in the reduction in both the expected equilibrium price and the price volatility from the respective base case levels. In the case of symmetric emitters, we get the following results: ob

P 0 ¼ c0 ðe0 −a0 þ B0 Þ;

ð53Þ

h i μ −a −B h i σ 21 ob ob 0 E P 1 ¼ 1 −1 1 ; Var P 1 ¼  2 : c1 þ θ N c−1 1 þθ

ð54Þ

Comparing Eqs. (53) and (54) to Eqs. (8) and (9), we note that when B0 h i ob ob N 0 and θ N 0, Pob 0 N P0, E P 1 bE½P 1  and Var[P1 ] b Var[P1]. This means that, net banking and net purchasing of option bundles by the regulated emitters simultaneously reduces the expected price level and the variance or volatility of permit price at time 1 from their respective base case levels. Under this combined mechanism, even B0 b 0, i.e., the regulated emitters choose to borrow permits from period 1 for usage in the current period, their purchased option bundles may still reduce h i ob both E P ob 1 and Var[P 1 ] from their base case levels, meaning that introducing option bundles is still effective in reducing the expected permit price level and the volatility of permit price simultaneously in a banking environment.

λ−

1 N ðμ 1 −a1 −B0 Þ2 þ σ 21 ¼ 0:  2 1þr 2N c−1 þ θ

ð57Þ

1

We recall that the regulator needs to impose a sufficiently tight cap a1 for time 1 so that B∗0 N 0 and θ∗ N 0 to stabilize the spot price and reduce the price volatility in the banking only or option only case. However, when both financial options and banking exist, the regulator may choose a relatively looser cap a1 for time 1 such that B∗0 may be negative (borrowing permits from time 1 for current usage), while the spot price is still stabilized and the price volatility is reduced from the base case level. The above suggests that combining financial options with banking and borrowing is more flexible in potentially allowing borrowing or choosing a cap while reducing the permit price volatility. In addition, the incentive for improving the economic efficiency of current emission abatement technology so as to reduce the total discounted emission reduction cost is kept under the combined approach: dTCob ∗/dc1 = λc−2 1 N 0, indicating that these regulated emitters have at least the same incentive to invest in enhancing emission abatement technologies in the combined case as in the option case. Furthermore, as banked/borrowed permits get used inter-period and the permits delivered from exercising the option bundles are created by unregulated sources, there are no extra emission allowances issued in the entire compliance period in the combined case. Finally, the total discounted cost of achieving the emission reduction target is further reduced by combining options and banking. Thus, this combined mechanism provides all the advantages of banking and financial options. We have demonstrated that introducing a market for properly designed emission permit options presents an innovative approach to emission permit price volatility mitigation under a cap-and-trade system. This approach also has the potential to reduce the overall cost for achieving the emission reduction target and offer the incentives to invest in improving emission abatement technology. Viswanathan (2010) points out that market innovation increases market efficiency and provides liquidity, but may lead to manipulation and inaccurate prices. While strict regulation would prevent manipulation and increase the price accuracy, but sacrifice liquidity. Having shown the potentials of the option bundles market in improving economic efficiency, we recognize that the introduction of such markets would require corresponding regulatory oversights for the new markets and incur additional operational and transactions costs. As suggested by Viswanathan (2010), in order for a cap-andtrade system to be successful, the regulator shall consider a hybrid approach to regulation which provides sufficient regulatory information to prevent market manipulation and, at the same time, allows for market innovation such as the options market proposed here. We envision that the most likely form for such option bundles markets to successfully develop is the over-the-counter trading with centralized settlement and clearing. Over-the-counter trading would encourage the growth in trading liquidity while centralized clearing and settlement would

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

11

facilitate regulatory oversights, mitigate price manipulation, and enhance transparency. 4. Numerical example In this section, we develop a numerical example to illustrate the comparative effects of the above four cases, based on the U.S. carbon emission profile. U.S. CO2 emissions in 2008 were about 6000 million metric tons (Mt) U.S. EPA (2010b). Although climate regulation may not regulate all CO2 emissions, for this example we work with 6000 Mt. In the U.S. there are about 3000 total electric utilities, although roughly 200 investor-owned electric utilities account for 40% of total electricity generation. In addition, petroleum refiners might under certain circumstances be regulated emitters, as well as other industrial sources of CO2 and other greenhouse gases. In a more detailed climate regulation scenario, there might be several hundred large regulated emitters and more than a thousand smaller regulated emitters. For development of a simple numerical example, we here approximate the emission sources as 1000 equal-sized regulated emitters. Let the number of regulated emitters be N = 1000, the initial business-as-usual emissions for each emitter be e0 = 6 Mt CO2, and the allocated quantity of permits at the beginning of the period be a0 = 5.9 Mt. A 15% reduction target over the compliance period, which might be 10 years or more, would correspond to an emission cap at the end of the period being a1 = 5.1 Mt. Let the expected business-as-usual emissions at the end of the period be μ1 = 5.5 Mt, with a standard deviation σ1 = 0.5 Mt. U.S. EPA (2010a) estimates an allowance (i.e., permit) price of about $11 per metric ton (t) for 2012. With a 15% cut in emission allowances, it estimates that the price would rise to about 23 $/t in 2027. Accordingly, for the base case we set P0 = 11 $/t and E½P 1  ¼ 23 $/t. By Eqs. (8) and (9), we estimate c0 = 1.1 × 10−4 $/t2 and c1 = 0.6 × 10−4 $/t2. We set the interest rate r = 0.02 and by Eq. (39), we estimate the price of a bundle of options λ = $ 100. All the parameters used in this numerical example are summarized in Table 1. For a system with combined banking and options, we solve Eqs. (56) ∗ = and (57) numerically, and get the optimal banked quantity Bob 0 0.03 Mt for each emitter, θob ∗ = 8509 units and the total discounted cost for each regulated emitters TCob ∗ = $ 4.45 million. With the same parameters, we solve Bb0 ∗ = 0.07 Mt for the banking only case and θo ∗ = 11361 units for the option only case. And the total discounted costs for each regulated emitter under the base case, banking case and option case are $ 5.26 million, $ 4.80 million and $ 4.49 million respectively. This illustrates that the combination of banking and options yields the lowest cost to achieve the carbon emission targets. We show the total discounted cost for the entire system of 1000 emitters in Fig. 5 for emission limits ranging from 5050 to 5150 Mt. The figure shows that if the reduction target is 15% (at 5100 Mt level), introducing financial options provides greater cost savings than banking-only. The slight difference between the options case and the combined case with options plus banking shows that the cost reductions mainly come from the trading of option bundles rather than from banking. Based on the above numbers, we illustrate the performance of the different approaches in reducing price difference, price volatility and total discounted cost in Table 2. The numbers in the brackets stand for the differences compared to the corresponding numbers in the base case. We note that bankable permits yield greater price difference than the financial options do, and that the combined approach is the most effective Table 1 Summary of parameters in the numerical example. N

e0

μ1

σ1

a0

a1

1000

6 Mt

5.5 Mt

0.5 Mt

5.9 Mt

5.1 Mt

c0

c1

P0(base)

E½P 1 ðbaseÞ

r

λ

1.1 × 10−4 $/t2

0.6 × 10−4 $/t2

11 $/t

23 $/t

0.02

$100

Fig. 5. Numerical example of optimal total cost for the entire system of achieving emission targets under different approaches.

one in reducing the permit price difference across different periods. Banking approach does not reduce permit price volatility while the financial options approach is most effective in that regard. The lowest total discounted cost in reaching the emission reduction target over the entire compliance period is achieved by the combined approach which offers both bankable permits and the trading of permit option bundles. A comparison of spot prices, variances, total discounted costs and changes of total discounted costs with respect to changing c1 in the base case, banking case, financial options case, and combined case is given in Table 3. The main findings are as follows. In the banking case, the positive net banking makes the price difference between time 0 and time 1 smaller than that of the base case, but the variance or the volatility is unchanged. The total discounted cost is lower than that of the base case, while the rate of change in total cost with respect to changing c1 is larger. In the financial options case, the positive net purchase of option bundles makes both the price difference and the price variance smaller than those of the base case. The total discounted cost is also reduced, while the rate of change in total cost with respect to changing c1 is larger than that of the base case. If we choose λ appropriately, the total discounted cost and the rate of change in total cost in the option case are lower than those of the banking case. Finally, in the combined case, there is more flexibility to choose the amount of banking or borrowing to reduce both the price difference and the price volatility. The combined scheme has the lowest total discounted cost among the four schemes, offering the benefits of both the simple banking approach and the financial options approach.

5. Conclusion In this paper, we investigate the role of emission permit options in managing the spot price risk of emission permit trading such as the price volatility in the carbon emission permit market under a cap-andtrade system. Through a two-compliance-time model, we show that with a tight emission cap imposed by the regulator, the trading of bundles of emission permit options can reduce both the spot price level and the price volatility, regardless of whether banking is allowed in the system or not3. In addition, the markets for emission permit options enable 3 While the option bundles proposed in our approach have a seemingly impractical feature of covering a continuum of strike prices, the insight that the trading of such options reduces the carbon permit price volatility through its effect of increasing price elasticity of the carbon-permit demands remains true when we consider option bundles with a set of properly chosen discrete strike price levels in a practical design.

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

12

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx

Table 2 Numerical example of performance of different price management approaches.

P 0 ; E½P 1  ($/t) Price difference: E½P 1 −P 0 ($/t) Price volatility ($/t) Total discounted cost ($ billion)

Base

Banking/borrowing

Financial options

Combined

11, 23 12 0.95 5.26

19.16, 19.54 0.38 (−11.62) 0.95 (0.00) 4.80 (−0.46)

11, 14.27 3.27 (−8.73) 0.56 (−0.39) 4.49 (−0.77)

14.38, 14.67 0.29 (−11.71) 0.63 (−0.32) 4.45 (−0.81)

a regulator to achieve some other important benefits simultaneously: directly linking incentives for the regulated emitters to invest in carbon abatement technologies to the prices of carbon emission options, providing incentives for unregulated emission sources to develop carbon reduction opportunities, and reducing the total discounted cost of achieving the emission reduction target. We also compare the option contract mechanism with its alternatives: a safety valve approach and a banking approach. While a ceiling on the emission permit price can indeed reduce the price volatility in the spot market, it may result in more carbon emissions than the desired cap level. As for the banking approach, it stabilizes the expected price levels of emission permits and reduces the total discounted cost of achieving the emission cap when a tight cap level is imposed. However, it neither necessarily reduces the volatility of emission permit price in future trading nor provides sufficient incentives for investments in carbon abatement technologies. Finally, we show that an approach combining the bankable permits and the trading of the proposed option bundles would possess the advantages of both mechanisms. Moreover, the combined approach offers the regulator with more flexibility in determining the desired emissioncap target, and this target can be achieved with lower social cost than that of the base case. While the introduction of the trading of such option bundles would require corresponding regulatory oversights for the new market and incur additional operational and transaction costs, we conclude that it presents a promising market-based approach to reduce emission permit price volatility. The proposed option bundles design demonstrates a potential advantage brought by financial innovations in making the capand-trade mechanism a successful policy design for achieving the environmental protection goal. The practical design and implementation of such options market and the corresponding regulatory rules require an in depth study and are left for future work. Acknowledgments We would like to thank the anonymous referees, seminar participants at Hitotsubashi University, and the Universidad Carlos III de Table 3 A summary comparison of price management approaches.

P0 E½ P 1  Var[P1] E½TC 1  TC dTC∗/dc1

Base

Banking/borrowing

c0(e0 − a0) c1(μ1 − a1)

c0(e0 − a0 + B0) c1(μ1 − a1 − B0)

c21 σ 21 N c1 ðμ 1 −a1 Þ2 2 c0 ðe0 −a0 Þ2 2

þ c2Nσh 1 c ðμ þ 1þr h i σ 1 ðμ −a Þ þ 2N 1þr 2 1

1

1

1

2 1

2

1 −a1 Þ

2

2

þ c2Nσ 1

2 1

i

2 1

c21 σ 21 N c1 ðμ 1 −a1 −B0 Þ2 2 c0 ðe0 −a0 þB0 Þ2 2

þ c2Nσh 1 c ðμ þ 1þr h i 1 ðμ −a −B Þ þ σ2N 1þr 2

Financial options

2 1

1

 2 0

1

1

1

þ c2Nσ 1

2 1

i

Combined

c0(e0 − a0)

c0(e0 − a0 + B0)

μ 1 −a1 c−1 þθ 1 σ 21

μ 1 −a1 −B0 c−1 þθ 1 2 σ1

E½TC 1 

N ðμ 1 −a1 Þ2 þσ 21

TC dTC∗/dc1

c0 ðe0 −a0 Þ2 2

2

2

N ðc−1 þθÞ 1

N ðc−1 þθÞ 1

c−1 þθ 1

λc−2 1

2

2

2 1

P0 E½ P 1  Var[P1]

2N ð

1 −a1 −B0 Þ

N ðμ 1 −a1 −B0 Þ2 þσ 21

Þ

2N ð

2

1 N ðμ −a Þ þσ þ λθ þ 1þr 2N ðc þθÞ 1

1 −1 1

2 1

c−1 þθ 1

Þ

c0 ðe0 −a0 þB0 Þ2 2

λc−2 1

2

1 N ðμ −a −B Þ þσ þ λθ þ 1þr 2N ðc þθÞ 1

1

0

−1 1

2 1

Madrid for the improved exposition of the paper. All remaining errors are our own. References Alberola, E., Chevallier, J., 2009. European carbon prices and banking restrictions: evidence from phase I (2005–2007). Energy J. 30 (3), 51–79. Aldy, J.E., Krupnick, A.J., Newell, R.G., Parry, I.W., Pizer, W.A., 2009. Designing Climate Mitigation Policy, (RFF DP 08-16). Bansal, V., Pruitt, S., Wei, K., 1989. An empirical reexamination of the impact of CBOE option initiation on the volatility and trading volume of the underlying equities: 1973– 1986. Financ. Rev. 24, 19–29. Bertrand, V., 2013. Modeling of emission allowance markets: a literature review. Working Paper Series. Climate Economics Chair. Bushnell, J.B., Chen, Y., 2009. Regulation, allocation, and leakage in cap-and-trade markets for CO2. Paper CSEMWP-183, Center for the Study of Energy Markets (URL http://repositories.cdlib.org/ucei/csem/CSEMWP-183). Cao, H., 1999. The effect of derivative assets on information acquisition and price behavior in a dynamic rational expectations model. Rev. Financ. Stud. 12, 131–163. Carmona, R., Fehr, M., Hinz, J., Porchet, A., 2010. Market design for emission trading schemes. SIAM Rev. 52 (3), 403–452. Celebi, M., Graves, F., 2009. CO2 price volatility: consequences and cures. Tech. Rep. The Brattle Group. Chao, H.-P., Wilson, R., 2004. Resource adequacy and market power mitigation via option contracts. Tech. Rep. Electric Power Research Institute and Stanford University. Chen, Y., Tseng, C.-L., 2011. Inducing clean technology in the electricity sector: tradable permits or carbon tax policies? Energy J. 32 (3), 149–174. Chesney, M., Taschini, L., 2008. The endogenous price dynamics of the emission allowances: an application to CO2 option pricing. Research Paper Series no. 08-02Swiss Finance Institute. Chevallier, J., Pen, Y.L., Sévi, B., 2011. Options introduction and volatility in the EU ETS. Resour. Energy Econ. 33, 855–880. Conrad, J., 1989. The price effect of option introduction. J. Financ. 44, 487–498. Cronshaw, M., Kruse, J., 1996. Regulated firms in pollution permit markets with banking. J. Regul. Econ. 9, 179–189. Dales, J., 1968. Pollution Property and Prices. University of Toronto Press. Damadoran, A., Lim, J., 1991. The effects of option listing on the underlying stocks' return processes. J. Bank. Financ. 15, 647–664. Daskalakis, G., Psychoyios, D., Markellos, R., 2009. Modeling CO2 emission allowance prices and derivatives: evidence from the European trading scheme. J. Bank. Financ. 33 (7), 1230–1241 (URL http://ssrn.com/abstract=912420). Eshel, D.M.D., 2005. Optimal allocation of tradable pollution rights and market structures. J. Regul. Econ. 28, 205–223. Fell, H., MacKenzie, I.A., Pizer, W.A., 2008. Prices versus quantities versus bankable quantities. Tech. Rep. Resources for the Future. Fleming, J., Ostdiek, B., 1999. The impact of energy derivatives on the crude oil market. Energy Econ. 21, 135–167. Grossman, S., 1988. An analysis of the implications for stock and futures price volatility of program trading and dynamic trading strategies. J. Bus. 61, 275–298. Grüll, G., Taschini, L., 2011. Cap-and-trade properties under different hybrid scheme designs. J. Environ. Econ. Manag. 61, 107–118. Hintermann, B., 2010. Allowance price drivers in the first phase of the EU ETS. J. Environ. Econ. Manag. 59, 43–56. Hintermann, B., 2013. An option pricing approach for CO2 allowances in the EU ETS. Working Paper. University of Zurich. Hitzemann, S., Uhrig-Homburg, M., 2010. Understanding the price dynamics of emission permits: a model for multiple trading periods. Working Paper. Karlsruhe Institute of Technology. Jacoby, H.D., Ellerman, A.D., 2004. The safety valve and climate policy. Energy Policy 32 (4), 481–491. Kijima, M., Maeda, A., Nishide, K., 2010. Equilibrium pricing of contingent claims in tradable permit markets. J. Futur. Mark. 30 (6), 559–589. Leconte, A., Pagano, T., 2010. Carbon derivatives: a destabilizing or a virtuous mechanism to build a carbon-free economy? The example of the European CO2 trading scheme. Working Paper. Lieberman, J.I., et al., 2007. Lieberman-Warner Climate Security Act of 2007. U.S. Library of Congress, http://thomas.loc.gov/cgi-bin/bdquery/z?d110:S.2191. Maeda, A., 2004. Impact of banking and forward contracts on tradable permit markets. Environ. Econ. Policy Stud. 6 (2), 81–102. Montgomery, W., 1972. Markets in licenses and efficient pollution control programs. J. Econ. Theory 5, 395–418. Napolitano, S., LaCount, M., Chartier, D., 2007. SO2 and NOx trading markets: providing flexibility and results. EM Mag. Air Waste Manag. Assoc. 22–26.

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001

L. Xu et al. / Energy Economics xxx (2014) xxx–xxx Newell, R., 2005. Managing permit markets to stabilize prices. Environ. Resour. Econ. 31, 133–157. Roll, R., Schwartz, E., Subrahmanyam, A., 2009. Options trading activity and firm valuation. J. Financ. Econ. 94, 345–360. Rubin, J., 1996. A model of intertemporal emission trading, banking, and borrowing. J. Environ. Econ. Manag. 31, 269–286. Schennach, S., 2000. The economics of pollution permit banking in the context of title IV of the 1990 Clean Air Act amendments. J. Environ. Econ. Manag. 40, 189–210. Seifert, J., Uhrig-Homburg, M., Wagner, M., 2008. Dynamic behavior of CO2 spot prices. J. Environ. Econ. Manag. 56, 180–194. Skinner, D., 1989. Options markets and stock return volatility. J. Financ. Econ. 23, 61–78. Stavins, R.N., 2008. Addressing climate change with a comprehensive US cap-and-trade system. Oxf. Rev. Econ. Policy 24 (2), 298–321.

13

Stein, J., 1987. Informational externalities and welfare-reducing speculation. J. Polit. Econ. 95, 1123–1145. Tietenberg, T., 1985. Emission Trading: An Exercise in Reforming Pollution Policy. Resources for the Future. Tietenberg, T.H., 2006. Emissions Trading: Principles and Practice, 2nd edition. RFF Press. U.S. EPA, 2010a. EPA Supplemental Analysis of the American Clean Energy and Security Act of 2009 (H.R. 2454), (Data annex). U.S. EPA, 2010b. Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990–2008, (U.S. EPA # 430-R-10-006). Viswanathan, S., 2010. Developing an efficient carbon emissions allowance market. Tech. Rep. Working Paper Series. Fuqua School of Business Duke University.

Please cite this article as: Xu, L., et al., Carbon emission permit price volatility reduction through financial options, Energy Econ. (2014), http:// dx.doi.org/10.1016/j.eneco.2014.06.001