Market specific seasonal trading behavior in NASDAQ OMX electricity options

Journal of Commodity Markets xxx (2018) 1–14

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Market specific seasonal trading behavior in NASDAQ OMX electricity options Jussi Nikkinen, Timo Rothovius * University of Vaasa, Department of Accounting and Finance, P.O. Box 700, FIN-65101, Vaasa, Finland

A R T I C L E I N F O

A B S T R A C T

JEL Classification: G10 G12 Q40

This study examines trading behavior in the NASDAQ OMX Commodities Europe electricity options' financial market using intraday data on individual option transactions. We postulate that the market differs from many other asset markets in that the main reason to trade is to hedge the price and quantity risks encountered in the physical market and because electricity is non-storable. Thus, in contrast to many other, more speculatively oriented markets, we find several disjunctive patterns in the trading of options. First, options on quarterly futures, providing the most flexible tools for hedging, are more heavily traded than options on yearly futures contracts. Second, trading activity is higher in options used to hedge against the coldest (i.e., peak) months. Third, trading activity is not higher prior to the expiry of options, implying that contracts are initiated early and not closed out prior to expiration. Fourth, trading activity does not decrease during the summer months. The results have several theoretical and practical implications.

Keywords: Trading activity Volume Seasonality Electricity Commodity Options

1. Introduction Seasonalities are a widely documented phenomenon in financial markets. The term refers to seasonal variations in returns, volatility, and trading volume time series and the phenomenon has been documented over various time intervals, including annually (the January, summer, and week of the year seasonalities), monthly (the turn of the month effect), weekly (the day-of-the-week effect), and daily (intraday effects). Recently, for example, Hong and Yu (2009) report on the summer seasonality; Draper and Paudyal (1997) and Sikes (2014) on the turn-of-the-year effect; Nikkinen et al. (2007) on the turn-of-the-month effect; H€ ogholm et al. (2011) on the day-of-theweek effect; and Abhyankar et al. (1997) on intraday effects. These findings have various implications for traders in financial and commodity markets, including effects on stock market risk premium (see e.g., Yadav and Pope, 1992), and valuation of commodity options (see e.g., Back et al., 2013). In this study, we investigate seasonality in the trading activity of electricity options1 using intraday data on all recorded option trades from a relatively liquid sample period of nearly six years in the NASDAQ OMX Commodities Europe financial market. In this the world's largest and most liquid financial market for financial derivatives on electricity, the electricity options provide practical tools for hedging2 against quantity and price risks encountered in the physical market. Hedging is important for both electricity producers, like

* Corresponding author. E-mail addresses: jn@uva.fi (J. Nikkinen), tr@uva.fi (T. Rothovius). Several previous studies have documented strong seasonality in spot electricity prices and the existence of peak periods (e.g. Lilliard and Acton, 1981; Lucia and Schwartz, 2002; Pardo et al., 2002). 2 In particular, options provide a vehicle to hedge against the unexpected peaks in electricity demand and spot prices that may occur, for example, during cold winter months (see, e.g., Pineda and Conejo, 2012). 1

https://doi.org/10.1016/j.jcomm.2018.05.002 Received 26 October 2017; Received in revised form 2 April 2018; Accepted 2 May 2018 Available online xxxx 2405-8513/© 2018 Elsevier B.V. All rights reserved.

Please cite this article in press as: Nikkinen, J., Rothovius, T., Market specific seasonal trading behavior in NASDAQ OMX electricity options, Journal of Commodity Markets (2018), https://doi.org/10.1016/j.jcomm.2018.05.002

J. Nikkinen, T. Rothovius

Journal of Commodity Markets xxx (2018) 1–14

electricity companies and their trading entities, and for the users of electricity, such as industrial companies. Furthermore, electricity is non-storable, which also makes the market different from other financial markets as well as most other commodity markets. Thus, in contrast to many other financial markets, we postulate that seasonalities in electricity markets differ from other, more speculative markets in several respects. Thus, based on the existing evidence on derivative markets, hedging and the unique features of the NASDAQ OMX Commodities Europe electricity options financial market, we present a set of testable hypotheses that are distinct to the electricity options. First, we hypothesize that options on quarterly futures contracts are more actively traded than options on yearly futures contracts. Second, we expect the trading volume to be higher for options on the quarterly futures for the first quarter of a year, which include the coldest winter months. According to our third hypothesis, trading activity in electricity options should not increase toward the expiry date of an option. Finally, we hypothesize that the trading activity is not lower in summer months compared to other months of the year. Examining the seasonalities in a unique market for electricity options deepens our understanding of the phenomena, separating those seasonalities that are common to all financial markets from those that can be attributed by the market or contract specific features. Specifically, our paper contributes to the existing literature in two major ways. First, to the best of our knowledge, this is the first study that examines seasonality in the trading activity of electricity options. Studies from electricity spot markets have documented seasonality in electricity prices, but none of those studies focus on the financial options market (see, e.g., Lilliard and Acton, 1981; Lucia and Schwartz, 2002; Pardo et al., 2002; Lucia and Pardo, 2010; Botterud et al., 2010; Escribano et al., 2011; Janczura et al., 2013; Mayer et al., 2015; and Hagfors et al., 2016). In many other financial markets, investigation of anomalies, seasonalities, liquidity, and market microstructure are among the most central research issues. Second, our study provides novel empirical evidence on the intraday behavior of the trading activity in the financial electricity option markets. In contrast to our study, previous studies using intraday data such as Huisman et al. (2007); Haugom et al. (2011); Birkelund et al. (2015); and Kiesel and Paraschiv (2017) do not use data from options markets. The majority of the studies using intraday data generally focus on issues such as volatility forecasting (see, e.g., Boller and Inder, 2002) rather than intraday trading patterns of financial derivatives. Our empirical results support the research hypotheses by showing that quarterly contracts, which provide a more flexible tool for hedging than yearly contracts, are more heavily traded. We also document that the trading activity is far higher on options for the coldest winter months, the time when the demand for electricity is at its peak. Our results also suggest that trading activity is not higher prior to the expiration of the option, implying that the contracts are initiated early and not closed out prior to expiration. Furthermore, we find that the trading activity does not decrease during the summer months as it does in many other asset markets. In addition to these main findings, we also document similar phenomena found in many other financial markets, such as a day-of-theweek effect (lower trading activity on Mondays), and, as evidenced by Abhyankar et al. (1997), a negative U-shape trading pattern over the course of a day. The implications of the study are important for the market participants. The results will provide a better understanding of the unique nature of commodities options markets, especially electricity option markets. This is important for market participants hedging their positions. For the same reason, the market efficiency is important, especially when some market participants such as electricity companies, are required to hedge their positions. The efficiency could be improved by increasing the trading, for example by attracting more speculative traders to enter the market, but even more importantly, by applying a market-making regime to reduce the bid-ask spread and ensuring a trade whenever needed by a hedger, especially for the contracts hedging the most volatile times. Market making would improve the situation at least for those contracts and/or certain specific periods. The results of our study may help to identify such option contracts and periods. The remainder of this paper is organized as follows. Section 2 presents an overview of the market environment in the NASDAQ OMX Commodities Europe financial market and develops the hypothesis. Section 3 describes the data. Section 4 presents the empirical methodologies used to examine the seasonality in trading activity. The empirical findings are presented in Section 5, and Section 6 concludes the paper. 2. NASDAQ OMX Commodities Europe financial market and research hypotheses 2.1. Market environment The Nordic physical electricity power market is the first international electricity market in the world. It consists of four Scandinavian countries: Norway (from 1993), Sweden (from 1996), Finland (from 1998) and Denmark (from 1999). Today, the NASDAQ OMX Commodities market (formerly Nord Pool), is the biggest international electricity market in the world, with 330 companies from 20 different countries trading on the exchange.3 The idea of the market is that each country can import or export the necessary power from or to a neighbor, if additional electricity supplies are required, or if there is a surplus of electricity. This would strengthen the security of electricity supply and ensure a better use of energy resources in the area. The primary sources of energy in the area are hydro, nuclear, and coal and the Nordic countries generate electricity from renewable sources at four times the average level of the OECD countries (Lindqvist, 2010). Naturally, the need for additional power varies from country to country and from period to period. To manage the risks associated with changes in the demand for electricity and physical market prices, the NASDAQ OMX

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Commodities offers a marketplace not only for spot electricity, but for financial instruments as well. The forward market was established in 1993 (it was then called the Statnett Marked AS). Today, the market offers different kinds of power derivatives, base and peak load futures, forwards, options, and contracts for difference (CfD). The reference price that is the underlying price, for these contracts is the system price of the physical market, which is the day-ahead price of electricity. The maximum trading time horizon is six years. Cash settlement is made throughout the trading- and/or the delivery period, starting at the due date of each contract. NASDAQ OMX Commodities acts as a clearinghouse, entering into all contracts as a counterpart, which guarantees the daily financial settlement. The trading is performed electronically, and is thus location independent and anonymous. It is well documented that electricity demand is subject to seasonal fluctuations (see e.g., Janczura et al., 2013). In Northern Europe, this is mostly because of changing weather, but also because of business activities. In some cases, the supply side may have seasonal patterns too, an example being the hydro units in Norway. These fluctuations result in increased demand and high prices during the winter time relative to the summer time. The volatility is also seasonal. On top of that, spot electricity prices often exhibit large, but infrequent, spikes, which are normally quite short-lived. The spikes are heavily concentrated in the winter months. 2.2. Hypotheses development In the NASDAQ OMX Europe Commodities market, the electricity options are primarily used for hedging. Electricity contracts for consumers are typically fixed price for a long period of time, so that the price, as well as quantity, risks remain with the electricity company. The biggest electricity users, such as steel producers, usually have a contract with flexible prices, so that they have to hedge against the price peaks themselves. These two groups are the biggest players in the derivative market, the same players that have the best information of future production and consumption of electricity. This leaves little room for outside speculators to play successfully against these dominant market participants. The market is also very concentrated,4 and producers have very strict rules about proprietary trading, and in many case companies are only allowed to hedge their positions. Furthermore, electricity is non-storable, which also makes the market different from other financial markets, including most other commodity markets.5 Thus, in contrast to many other financial markets, we postulate that seasonality in electricity markets affects the trading behavior of derivatives so that the trading behavior differs from other more speculative markets in several respects. Especially in the Scandinavian electricity market, there is considerable seasonal variation in demand for electricity. For example, the peak demand is oriented toward the coldest winter months, usually around the first quarter of the calendar year. The peak prices during these months may be up to several times the average spot price during the year. In these times, both the demand and spot prices are at a very high level.6 Given that information, first, it is important for electricity market participants to hedge against increased quantity and price risks according to the annual variation. Second, the use of options, instead of, or in addition to, futures contracts, provides flexibility (see e.g., Moschini and Lapan, 1995). Given the availability of the underlying base load futures (quarterly and yearly contracts), we expect options on the quarterly futures contracts to be more actively traded than options on the yearly futures contracts due to their greater flexibility and ability to hedge for the winter months. When a hedger exercises an option, he or she will enter into a futures contract, and the shorter the futures contract, the more exactly he or she can target the time frame to be hedged. This leads us to propose our first hypothesis. H1.

Options on the quarterly futures contracts are more actively traded than options on the yearly futures contracts.

Furthermore the above reasoning leads us to expect that the increased demand for contracts used to hedge against the coldest winter months (options on the first quarter futures, when the demand for electricity is at its peak) can be observed in the market. This leads to our second hypothesis. H2.

Trading volume is higher for options on quarterly futures for the first quarter of the year.

Brown and Toft (2002) note that the notional values of optimal forward hedges increase when the hedging horizon becomes shorter. In the NASDAQ OMX electricity derivatives markets, hedgers can establish forward hedges via option contracts, since upon expiry, the hedger with a long call (put) position is entitled to a long (short) position in the underlying quarterly or annual forward contract.7 If there is a relatively large number of hedgers in the market, the demand for longer maturity options may be expected to be higher than the demand for shorter maturity options. Brown and Toft (2002) illustrate that firms with long hedging horizons use more options than those with short hedging horizons.8 Thus, while in derivative markets in general, short maturity options are typically the most actively traded (see, e.g., Stephan and Whaley, 1990 and Wei and Zheng, 2010), our third hypothesis in the NASDAQ OMX electricity derivatives

4 For example, the biggest producer, Vattenfall, accounts for about 22 percent of the total electricity supply in the whole Nordic area, and the three biggest companies about 45 percent together. 5 It is possible to store electricity by pumping water from a lower elevation to a higher elevation, called pumped-storage hydroelectricity, with energy efficiency between 70 and 80 percent. However, this is possible for only those few producers having sufficient water reservoirs, and it accounts for only a small fraction of electricity demand. 6 Brown and Toft (2002) show that the most important factors in constructing optimal hedges are the correlation between price and quantity and the respective volatilities of price and quantity risk. Their argument is that if the correlation between demand and spot prices increases, the benefits of hedging increase. 7 Brown and Toft (2002) conclude that firms may be reluctant to undertake a large locked hedges over long horizons since it may be difficult to forecast exposure (quantity) accurately. Instead, their hedges are more likely to be composed of long positions in options. 8 In derivative markets, short maturity options are typically the most actively traded (see, e.g., Stephan and Whaley, 1990), whereas longer maturity options are less traded, i.e., there is a negative relationship between the maturity of the option and trading activity. This common phenomenon in derivative markets is recently documented, for example, by Wei and Zheng (2010) for individual equity options.

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markets states: H3.

Trading activity in electricity options does not increase toward the expiration.

Trading in speculative financial markets, in general, decreases during the summer months. For example, Hong and Yu (2009) document that stock turnover is lower during the summer because of vacations of market participants. However, we would not expect such phenomena to exist in a market where the primary reason for trading is hedging, even though the summer holidays in Scandinavia are during the summer, most often in July, and trading, for example, in stock markets decreases during the summer (see Hong and Yu, 2009). Theoretical models suggest hedging should increase gradually, with increasing speed, during the year (see e.g., Brown and Toft, 2002). Thus, our fourth hypothesis is that the trading in the electricity option market should not decrease during the summer months. H4.

Trading activity is not lower in summer months.

In many respects other than those described above, electricity option markets can be expected to behave like other derivative markets. We expect, for example, to observe the day-of-the-week effect, which is one of the most investigated calendar anomalies affecting financial markets. For example, in the U.S. stock market, the common observation is that returns are lower on Mondays (see e.g., Cross, 1973; French, 1980; Keim and Stambaugh, 1984; Rogalski, 1984; Aggarwal and Rivoli, 1989), and trading activity is lower on Fridays and higher on Tuesdays (see e.g., Chordial and Roll, 2001). The day-of-the-week effect has been widely documented in various other financial markets, including financial derivative markets. We also expect trading activity to be lower at the beginning and at the end of the trading day, which has also been documented previously (see e.g., Abhyankar et al., 1997). The hypotheses of our study are particularly relevant from the point of view of the commodity research, since the electricity markets have unique characteristics, as explained by Benth et al. (2013) and Janczura et al. (2013), who point out that the price process in the electricity markets shows seasonalities, mean reversion and spikes, as well as that the electricity is non-storable, unlike most other commodities.

3. Data description The data used in this study were provided by the NASDAQ OMX Commodities, which is the brand name for the commodities division within the NASDAQ OMX Group. The NASDAQ OMX Commodities is generally regarded as the most mature and stable power market in the world, being the world's largest and most liquid power exchange.9 Financially settled electricity futures were introduced in 1997 for both base and peak load. The underlying is a 24-h average day-ahead base peak load electricity price, making the spot electricity market, in fact, a day-ahead market. This is obvious since the system operator needs advance notice to verify the feasibility of the schedule. Options trading commenced in 1999, with the same delivery periods as the simultaneously traded futures contracts. Underlying the options are base load futures, and both quarterly and yearly contracts. The futures contracts have a delivery period of one month, a quarter and a year. The cash settled monthly futures mature one day prior to the end of the delivery month, while the other futures do so three trading days before the commencement of the delivery period. The quarterly and annual contracts are replaced by corresponding positions in monthly futures at maturity. On the Nordic power option market, the underlying is the relevant forward contract for the corresponding quarter or year. The unit of trading and the minimum contract and lot size is 1 MW with minimum tick size of one eurocent. There are five contracts traded at a time, the first with December and the end of the closest quarter delivery dates, and the next year with December and two quarterly delivery contracts. There are four strike prices around at-the-money (ATM) with an interval of 1 euro, with an expiry day of the third Thursday of the month, as in most other option markets. Now only European style options are available, and they are traded continuously between 8.00 and 15.30 CET. According to several studies (e.g. Ebenezer and Kaul, 2008), the trading hours are relevant determinants of daily trading volume. The options are automatically exercised at expiry if worth at least five eurocents, and each option contract is delivered as the underlying forward contract, quarterly or yearly. The counterparty risk is eliminated by the clearinghouse acting itself as a counterparty in all trades. The sample period used in the study starts on January 1st, 2006 and ends on September 22nd, 2011, which represent a relatively liquid trading period in the NASDAQ OMX Commodities Europe electricity options' financial market. The data consist of 4827 intraday trade observations. Thus, we use all individual option contracts during the sample period, recorded and provided by the NASDAQ OMX Commodities Europe. The descriptive statistics are presented in Table 1, which include summary statistics for call and put options during the sample period. As can be seen from the table, average trading volumes, in monetary terms, are higher for call options than for put options. However, the average number of contracts for calls is less than that for the puts. Looking at the moneyness of options, measured using the delta of an option, indicates that both call and put options are traded out-of-the money. This is broadly consistent, for example, with suggestions by Day and Lewis (1988) that ATM and out-of-the-money (OTM) options are typically the most actively traded contracts. The maturities of options are 0.39 and 0.41 years on average for calls and puts respectively and range close to two years. Option implied volatilities are computed using the Black76 option pricing model, which is also applied by the exchange for the calculation of margins. The mean implied volatility is 0.397 for calls and 0.372 for puts. Thus, implied volatilities seem to be slightly higher for call options than for put options, on average. This is opposite to what has been observed in equity options markets (see, e.g. Gemmill, 1996).

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Table 1 Descriptive statistics. This table presents summary statistics for call and put options, for a total number of 4827 intraday trade observations. Implied volatility is based on the Black76 model. Moneyness is measured using the delta of an option. Maturity of option is time-to-expiration expressed in years. Variable Panel A. Call options (N ¼ 2652) Volume (Euro) log (Volume) # of contracts log (# of contracts) Option price Implied volatility Moneyness Maturity Panel B. Put options (N ¼ 2175) Volume log (Volume) # of contracts log (# of contracts) Option price Implied volatility Moneyness Maturity

Mean

Std Dev

Min

Max

94.732 4.000 43.044 3.488 2.414 0.397 0.365 0.393

112.839 1.196 38.269 0.792 2.021 0.114 0.157 0.347

0.010 4.605 1.000 0.000 0.010 0.100 0.004 0.003

1417.000 7.256 500.000 6.215 18.420 1.200 0.995 1.959

73.750 3.686 47.045 3.525 1.778 0.372 0.266 0.414

94.642 1.282 46.876 0.841 1.639 0.097 0.138 0.367

0.030 3.507 1.000 0.000 0.010 0.100 0.994 0.003

1265.000 7.143 600.000 6.397 27.050 0.858 0.003 1.957

4. Methodology 4.1. Seasonality in trading volume and trade size In order to examine the relationship between trading volume and trade size, and seasonal and other explanatory variables, the following linear regression models are estimated:

gm ¼ Wαm þ εm ;

(1)

where gm is a ðn  1Þ vector of the volume measure, i.e. the log of trading volume (m ¼ 1), log of number of contracts (m ¼ 2), or trade price (implied volatility) (m ¼ 3), W is a ðn  32Þ design matrix of explanatory variables and αm is a ð32  1Þ vector of parameters to be estimated and εm a ðn  1Þ vector of random errors. The basic set of 26 seasonal explanatory variables contains Intercept, eleven month dummy variables, four weekday dummy variables, seven trading hour dummy variables, and five year dummies. In addition, six option contract specific variables are defined. These are: moneyness, maturity, expiration week, expiration month, underlying type, and expiration cycle. The option moneyness is measured using the delta of an option. The maturity of an option is time-to-expiration expressed in years, expiration week and expiration month are dummies indicating one week and one month before the expiration date, respectively and quarter is a dummy variable having the value 1 if the underlying instrument is a quarterly futures contract and otherwise zero. Winter is a dummy variable having the value 1 if the underlying futures contract expires during the first quarter of the year and otherwise zero. A positive value for αkm suggests a positive relation between the measure m and the kth explanatory variable. In this analysis, we are particularly interested in six option-contract-specific variables. In the electricity market, much of the trading may be related to hedging behavior. If this is the case, we expect, in line with our first hypothesis, that the coefficients for the quarter dummy variable will be positive for trading volume and trade size. Moreover, we expect, according to the second hypothesis, that the coefficient for trading volume will be higher for the first quarter of a year (i.e., the winter months). Further, according to the third hypotheses, the coefficients for the expiration month and expiration week dummies are non-positive and maturity non-negative due to the hedging nature of the market. Finally, we expect that the variation documented previously in the electricity spot markets (see, e.g., Pardo et al., 2002) will also be reflected in the coefficients for the monthly dummy variables indicating some seasonality across months. However, according to our fourth hypotheses, the dummies for the summer months are not expected to be lower than the dummies for the other months. Regarding the basic seasonal variables, if there is a day-of-the-week effect expressed as reduced trading activity on Mondays compared to the other weekdays, it is expected that the coefficient for the Monday dummy will be negative (see, e.g., Kiymaza and Berument, 2003). In addition, trading is likely to be less active soon after opening and shortly before the close of a trading session (see e.g. Abhyankar et al., 1997), as well as during the lunch hour, which should be seen in the hourly dummies. With respect to the sign of the yearly dummy variables, we do not have any particular expectations, although the global financial crisis of 2007/2008 and the subsequent sovereign debt crisis are likely to have affected the production and consumption of electricity and, consequently, trading activity in the electricity options market. With respect to multicollinearity, an analysis of variance inflation factors (VIF) indicates multicollinearity is not a problem in the analysis of this study (see e.g., Judge et al., 1988, 868–871).

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4.2. Seasonality in trading probability In order to examine the seasonality in hourly trading probability, that is, the likelihood that a trade occurs within a trading hour, the following probability model is estimated:


 PrðtradeÞ ¼ Φ x0i β ;

i ¼ 1; 2; :::; T;

(2)

where PrðtradeÞ represents a probability that a trade occurs within a trading hour and, and xi is a ð1  26Þ vector of seasonal attributes (as in Eq. (1)), which are Intercept, month dummy variables (11), weekday dummy variables (4), trading hour dummy variables (7), and year dummies (5). β is a parameter vector and Φð⋅Þ is a cumulative standard normal distribution function. The model is estimated by maximizing the following likelihood function:

ln ℓ ¼

T X 
 
  Ii ln Φ x0i β þ ð1  Ii Þln 1  Φ x0i β ;

(3)

i¼1

b is where the indicator variable Ii has a value of one if a trade occurs during the ith trading hour. The maximum likelihood estimator β consistent, asymptotically efficient and asymptotically normally distributed (see Amemiya, 1986, pp. 270–273). Our expectations on the signs of the seasonal variables are based on the same logic as in model (1). It is expected that some monthly variation is present in trading probabilities. According to our hypothesis, we do not expect to find the summer holiday effect. However, we expect to document the day-of-the-week effect in trading probabilities. In addition, we expect trading to be less active after opening and before closing of trading session and during the lunch hour, implying negative coefficient estimates. b b b ℓðωÞ, where ℓðΩÞ is the value of the likelihood function The McFadden likelihood ratio index is defined as LRI ¼ 1  ln ℓðΩÞ=ln b evaluated at maximum likelihood estimates and ℓðωÞ is the maximum value of the likelihood function under the hypothesis that the parameter estimates except that for the intercept are together equal to zero are given. The McKelvey and Zavoina (1975) pseudo-R2 is also provided. Furthermore, the following Poisson model is estimated for the hourly number of trades:


 eλi λyi i ; Pr # of trade ¼ yi ¼ yi !

i ¼ 1; 2; :::; T; yi ¼ 0; 1; 2; …

(4)

ln yi ¼ γ0 xi ;

where yi is the number of trades occurring at the ith trading hour, xi is a ð1  26Þ variable vector as defined in model (1) and γ is the corresponding parameter vector. Maximizing the following likelihood function produces the parameter estimates:

ln ℓ ¼

T X ½λi þ yi γ0 xi  ln yi !:

(5)

i¼1

The maximum likelihood estimator b γ is consistent, asymptotically efficient and asymptotically normally distributed. A positive sign of γ k implies the positive relation between the number of trades per hour and the kth explanatory variable. The importance of a variable added to a model containing only the intercept term is statistically tested using the likelihood ratio test. In the case of model (3), our expectations regarding the signs are similar to those in the case of models (1) and (2). The coefficients for the monthly dummy variables are expected to show some variation and we expect to observe that the day-of-the-week effect, i.e. the coefficient for the Monday dummy is negative. In the same way, trading is expected to be less active shortly after the opening and before the close of a trading session. 5. Empirical results 5.1. Trading volume and trade size Table 2 reports the estimation results of the regression equation (1) for trade sizes, that is, number of contracts, and Table 3 reports the same for trading volumes as measured in euros. The tabulated results show that although only some of the contract specific variables explain variations in trading volume (Table 2), they are all statistically highly significant in explaining the trading volume in euros (Table 3). In particular, we find that the coefficient for the quarterly dummy is positive for both trade sizes as well as trading volumes. This clearly suggests that there is a greater demand for the options on the quarterly futures compared to the options on the yearly futures. This is in accordance with our first hypothesis that the options on the quarterly futures contracts are more actively traded than the options on the yearly contracts, due to their greater flexibility in hedging. When a hedger exercises an option, he or she will enter into a futures contract, and the shorter the futures contract, the more exactly he or she can target the time frame to be hedged. The winter dummy behaves a little differently. First, the findings in Table 2 show that it is not significant for trade sizes (number of contracts traded). However, this is quite obvious, since the price and volatility of electricity is far greater in the winter time, so the contracts for the winter time should also be far more valuable. In other words, one contract hedges against a far greater economic risk. 6

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Table 2 Seasonality in trade sizes (number of contracts). The following linear regression models are estimated: gm ¼ Wαm þ εm , where gm is a ðn  1Þ vector of ln of number of contracts, W is a ðn  32Þ design matrix of explanatory variables and αm is a ð32  1Þ vector of parameters to be estimated and εm a ðn  1Þ vector of random errors. The basic set of explanatory seasonal variables is defined as previously in model (1). In addition, six option contract specific variables are defined. These are moneyness, maturity, expiration week, expiration month, underlying type, and expiration cycle. Option moneyness is measured using the delta of an option. The maturity of option is time-to-expiration expressed in years, expiration week and expiration month are dummy indicating one week and one month before the expiration date, respectively and quarter is a dummy variable having value 1 if the underlying is a quarterly futures contract and otherwise zero. Winter is a dummy variable having the value 1 if the underlying futures contract expires during the first quarter of the year and otherwise zero. The White heteroscedasticity consistent covariance matrix is used. Call options

Put Options

Es.

t-value

p-value

Es.

t-value

p-value

Intercept

3.630

30.95

0.000

3.595

30.46

0.000

Monthly variation Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

0.096 0.016 0.166 0.125 0.183 0.120 0.078 0.104 0.073 0.099 0.100

0.95 0.16 1.66 1.19 1.80 1.12 0.68 0.99 0.68 0.94 0.96

0.342 0.874 0.097 0.236 0.071 0.262 0.498 0.321 0.495 0.345 0.335

0.175 0.167 0.054 0.031 0.089 0.055 0.042 0.119 0.011 0.151 0.004

1.64 1.36 0.50 0.28 0.89 0.51 0.39 1.18 0.10 1.41 0.04

0.100 0.175 0.615 0.779 0.372 0.607 0.700 0.240 0.921 0.160 0.968

Day-of-the-week effect Mon Tue Wed Thu

0.161 0.064 0.049 0.038

2.86 1.38 1.10 0.82

0.004 0.168 0.272 0.411

0.019 0.141 0.037 0.002

0.29 2.68 0.67 0.04

0.772 0.007 0.501 0.967

Intraday variation 8–9 9–10 10–11 12–13 13–14 14–15 15–16

0.288 0.160 0.079 0.082 0.117 0.166 0.234

2.97 2.81 1.50 1.43 2.12 3.40 3.96

0.003 0.005 0.135 0.153 0.034 0.001 0.000

0.219 0.009 0.078 0.010 0.033 0.088 0.264

1.94 0.13 1.48 0.16 0.61 1.78 3.78

0.053 0.895 0.138 0.870 0.541 0.076 0.000

Annual variation Year07 Year08 Year09 Year10 Year11

0.091 0.109 0.080 0.222 0.233

2.17 2.15 1.57 4.67 3.28

0.030 0.032 0.116 0.000 0.001

0.144 0.348 0.066 0.125 0.054

3.12 6.57 1.24 2.08 0.57

0.002 0.000 0.215 0.038 0.565

Contract specific variables Quarter Winter Maturity Exp_week Exp_month Moneyness

0.195 0.021 0.235 0.143 0.024 0.413

4.08 0.30 3.69 1.39 0.45 3.83

0.000 0.764 0.000 0.164 0.652 0.000

0.436 0.063 0.063 0.362 0.036 0.504

8.63 0.82 1.13 1.57 0.54 3.32

0.000 0.412 0.260 0.118 0.589 0.001

Adj. R sqr. F – value p – value

0.08 7.76 0.000

0.13 10.81 0.000

This is evident in Table 3, from which we can see that the coefficients for the winter dummies are statistically highly significant for both call and put options, implying that the trading volume in euros is clearly higher for the contracts hedging against the winter time. This is in line with our second hypothesis. This may also partly explain why the adjusted R-squares, 0.47 and 0.48 for call and put regressions, are far higher for the trading volumes compared to trade sizes, at 0.08 and 0.13 correspondingly. The maturity variables for the trade sizes are highly significant for call options. The negative coefficient suggests that the longer the maturity, the less trading; a finding in accordance with earlier literature. However, for the put options, the coefficient, although negative in sign, is not significant. It may be that the put options, if used for hedging, are traded earlier, or it may also indicate that trading is not increased close to maturity because of the closing out of the option positions. In contrast to trade sizes, the maturity coefficient estimates for trading volume in euros are positive and highly significant for both put and call options. The time value of an option is naturally

7

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Journal of Commodity Markets xxx (2018) 1–14

Table 3 Seasonality in trading volume in euros. The following linear regression models are estimated: gm ¼ Wαm þ εm , where gm is a ðn  1Þ vector of ln of trading volume in euros, W is a ðn  32Þ design matrix of explanatory variables and αm is a ð32  1Þ vector of parameters to be estimated and εm a ðn  1Þ vector of random errors. The basic set of explanatory seasonal variables is defined as previously in model (1). In addition, six option contract specific variables are defined. These are moneyness, maturity, ex piration week, expiration month, underlying type, and expiration cycle. Option moneyness is measured using the delta of an option. The maturity of an option is time-toeqxpiration expressed in years, expiration week and expiration month are dummies indicating one week and one month before the expiration date respectively, and quarter is a dummy variable having the value 1 if the underlying is a quarterly futures contract and otherwise zero. Winter is a dummy variable having the value 1 if the underlying futures contract expires during the first quarter of the year and otherwise zero. The White heteroscedasticity consistent covariance matrix is used. Call options

Put Options

Es.

t-value

p-value

Es.

t-value

p-value

Intercept

1.875

12.2

0.000

1.605

11.55

0.000

Monthly variation Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

0.306 0.270 0.475 0.442 0.532 0.415 0.555 0.592 0.514 0.347 0.291

2.45 2.00 3.78 3.38 4.12 3.08 4.01 4.45 3.68 2.56 2.10

0.014 0.046 0.000 0.001 0.000 0.002 0.000 0.000 0.000 0.011 0.036

0.311 0.112 0.169 0.228 0.387 0.406 0.521 0.594 0.322 0.012 0.115

2.51 0.76 1.33 1.75 3.19 3.23 4.00 4.84 2.23 0.09 0.93

0.012 0.445 0.185 0.080 0.001 0.001 0.000 0.000 0.026 0.926 0.353

Day-of-the-week effect Mon Tue Wed Thu

0.161 0.056 0.059 0.080

2.43 1.06 1.14 1.50

0.015 0.289 0.255 0.133

0.107 0.178 0.021 0.065

1.32 2.95 0.34 0.99

0.188 0.003 0.735 0.321

Intraday variation 8–9 9–10 10–11 12–13 13–14 14–15 15–16

0.163 0.096 0.057 0.063 0.104 0.167 0.266

1.56 1.44 0.97 0.95 1.65 2.95 3.80

0.119 0.151 0.333 0.344 0.099 0.003 0.000

0.137 0.195 0.011 0.020 0.052 0.058 0.292

0.98 2.62 0.17 0.28 0.82 0.94 3.59

0.328 0.009 0.863 0.778 0.414 0.346 0.000

Annual variation Year07 Year08 Year09 Year10 Year11

0.148 0.153 0.114 0.242 0.168

3.05 2.64 2.05 4.36 2.23

0.002 0.008 0.040 0.000 0.026

0.349 0.143 0.089 0.249 0.058

6.50 2.25 1.46 3.20 0.56

0.000 0.025 0.144 0.001 0.574

Contract specific variables Quarter Winter Maturity Exp_week Exp_month Moneyness

0.312 0.348 0.550 0.954 0.611 4.240

5.88 4.26 7.60 6.69 8.87 30.98

0.000 0.000 0.000 0.000 0.000 0.000

0.666 0.254 1.000 1.759 0.626 5.046

11.24 2.56 15.19 4.16 7.72 22.07

0.000 0.010 0.000 0.000 0.000 0.000

Adj. R sqr. F – value p – value

0.47 71.44 0.000

0.48 60.69 0.000

higher the longer the maturity, but our result may also suggest that the contracts are not closed out near the end of the maturity. This view is further enhanced by the coefficients for the expiration week and month dummies, which are negative in every case, although significant only for trading volume. These findings collectively provide support for our third hypothesis according to which the trading activity is not higher prior to expiration of an option. This is consistent with the idea that hedgers can enter into the hedge earlier when using options instead of futures, since an option is a right, unlike a futures contract, which is an obligation. The month dummies indicate that trading volumes exhibit some monthly variation, especially when the trading volume is considered (see Tables 2 and 3). Our findings support the fourth hypothesis, according to which trading in the electricity option market should not decrease in the summer months. In fact, the coefficients of the monthly dummies increase slightly during the summer time to a peak in August, after which they again decrease toward the end of the year.

8

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Journal of Commodity Markets xxx (2018) 1–14

With respect to the moneyness of call and put options, measured using delta, Tables 2 and 3 document the negative relationship between moneyness and trading volume measures. Since the delta is positive for call options and negative for put options, the results indicate that an increase in option moneyness leads to a reduction in trading volume. Tables 2 and 3 also reflect that the coefficient estimates for the Monday dummies are negative and significant in the case of call options and the Tuesday dummies are positive and significant for put options. Both these findings hold for trade size and also trading volume. This finding provides partial support for the existence of a day-of-the-week effect, and is broadly consistent with the observations from many other financial markets, according to which returns are lower on Mondays and trading activity is lower on Fridays and higher on Tuesdays on average (Chordial and Roll, 2001). With respect to the intraday variation, particularly the coefficients of the early (0800–1000) and late afternoon (1400–1600) trading hours are negative and statistically significant. This observation is consistent for both calls and puts, and for trade sizes and trading volume. This is in line with our expectation of an hourly variation, stating that trading activity is lower at the beginning and end of the day. The same phenomena is evidenced also in previous research, see for example Abhyankar et al. (1997), who discuss a negative Ushape intraday trading pattern. Table 4 presents results for trade prices, measured using implied volatilities. The observed results are consistent with the results reported in Tables 2 and 3. Looking at the table shows interestingly that in the case of implied volatility the coefficients for the quarter and winter dummies are positive suggesting that the corresponding options are traded at higher prices. Similarly, implied volatilities indicate that short maturity options have higher prices than long maturity options, relatively. Furthermore, the trade prices seem to be lower afternoon between 1200 and 1400. During the crises years 2008 and 2009 the options were generally traded at higher prices compared to other years. While the yearly dummies in Tables 2–4 are quite ambiguous, they may reveal some effects of the financial crisis. The coefficient estimates are negative and statistically significant for trade size in 2008, and more or less for trading volume in 2009, whereas for 2010, all of the estimates are clearly positive and statistically significant, and for 2011 they are positive and statistically significant for call options. It seems that trading decreased during the crises, maybe due to the lack of a counterpart, and bounced back after the crises. In Table 5, the possible effects of the global financial crisis is examined further by excluding years 2008 and 2009 from the analysis. Thus, Table 5 provides the estimation results of the regression equation (1) for trading volumes measured in euros, excluding the crises years. The results are well in line with those of Table 3. Thus, it can be concluded that the yearly dummy variables are able to capture the effect of the financial crisis.

5.2. Trading probabilities Table 6 reports the results regarding the seasonality in trading probabilities, that is, the likelihood that a trade occurs within a trading hour (the probit regression) and the likelihood of a certain number of trades occurring within a trading hour (the Poisson regression). For the call (put) options, the results reported in Panel A (Panel B) show that the hourly trading probability is 19.27% (16.55%) and the average number of trades per hour is 0.32 (0.26). These figures indicate that both call and put options are thinly traded, which may be partly explained by the lack of market making. The coefficients for the month dummy variables vary considerably across months, both in the probit and Poisson regressions, indicating seasonality both in the likelihood of trading and number of trades (see Table 4). While it has been documented that trading in speculative financial markets decreases during the summer months (see, e.g., Hong and Yu, 2009), the coefficients for the summer months June, July, and August, however, are not negative and do not seem to be lower than the coefficients for the other months. This finding is consistent with the results presented in Tables 2 and 3, and supports the hypothesis suggesting that trading activity is not lower during the summer months. Regarding the weekday dummies, the coefficient estimates for the Monday dummy are negative and significant in the case of both put and call options, and for the Wednesday dummy positive and significant for put options, suggesting a significantly lower trading probability on Mondays for all options, but a higher probability on Wednesdays for put options. With respect to the trading hours, the probit and Poisson regressions reveal that the coefficient estimates for the early trading hours (0800–0900) and (0900–1000) are negative and significant, whereas the coefficients for the late trading hours (1400–1500) and (1500–1600) are positive and highly significant. The coefficients for the yearly dummy variables are all negative and also significant since the year 2008. This shows that there is a decreasing trend in trading activity toward the end of the sample period. It may also indicate that the global financial crisis of 2007/ 2008 and the subsequent debt crisis caused a reduction in trading activity in the electricity options market. In summary, the results regarding the seasonality in trading probability and the probability of a certain number of trades are consistent with those from the trade size and trading volume regressions. It is important to remember, however, that they measure slightly different aspects of trading activity and reveal some complementary features. While the trade size and trading volume regressions aim to explain how the size of the trade (in # of contracts or in euros) is influenced by seasonal variables, the latter models measure how the probability of trading is affected by seasonality. Collectively, the results reveal that although trade size in the number of contracts does not seem to exhibit much annual variation, trading probabilities seem to increase at first in October and November, for instance, which might suggest that positions are fine-tuned for the winter months. Trading probabilities also seem to increase in January and February, which in turn might indicate that positions are adjusted during the cold winter months. While we are not able to rigorously test the validity of these interpretations, our results clearly establish the existence of systematic market specific seasonal trading behavior in the NASDAQ OMX Commodities Europe electricity options' financial market. 9

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Journal of Commodity Markets xxx (2018) 1–14

Table 4 Seasonality in trade prices (implied volatility). The following linear regression models are estimated: gm ¼ Wαm þ εm , where gm is a ðn  1Þ vector of the trade price (implied volatility), W is a ðn  32Þ design matrix of explanatory variables and αm is a ð32  1Þ vector of parameters to be estimated and εm a ðn  1Þ vector of random errors. The basic set of explanatory seasonal variables is defined as previously in model (1). In addition, six option contract specific variables are defined. These are moneyness, maturity, expiration week, expiration month, underlying type, and expiration cycle. Option moneyness is measured using the delta of an option. The maturity of option is time-to-expiration expressed in years, expiration week and expiration month are dummy indicating one week and one month before the expiration date, respectively and quarter is a dummy variable having value 1 if the underlying is a quarterly futures contract and otherwise zero. Winter is a dummy variable having value 1 if the underlying futures contract expires during the first quarter of the year and otherwise zero. Call options

Put Options

Es.

t-value

p-value

Es.

t-value

p-value

Intercept

0.368

21.66

0.000

0.349

38.44

0.000

Monthly variation Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

0.021 0.031 0.029 0.021 0.017 0.000 0.023 0.020 0.018 0.005 0.011

1.82 2.35 2.21 1.71 1.41 0.02 1.87 1.50 1.18 0.38 0.77

0.069 0.019 0.027 0.088 0.160 0.983 0.062 0.134 0.237 0.703 0.441

0.007 0.035 0.014 0.020 0.012 0.003 0.015 0.012 0.012 0.007 0.013

0.89 3.97 1.68 2.31 1.68 0.42 1.79 1.59 1.21 0.86 1.56

0.373 0.000 0.093 0.021 0.094 0.671 0.074 0.112 0.228 0.389 0.119

Mon Tue Wed Thu

0.008 0.004 0.007 0.004

1.33 0.91 1.41 0.78

0.184 0.361 0.158 0.433

0.003 0.002 0.005 0.005

0.49 0.46 1.26 1.20

0.621 0.649 0.208 0.229

8–9 9–10 10–11 12–13 13–14 14–15 15–16

0.004 0.007 0.006 0.009 0.010 0.000 0.005

0.53 1.12 1.16 1.63 1.77 0.09 1.02

0.597 0.264 0.246 0.103 0.076 0.929 0.307

0.007 0.008 0.003 0.012 0.009 0.003 0.005

0.93 1.25 0.54 2.15 1.59 0.57 0.83

0.353 0.212 0.593 0.031 0.112 0.566 0.409

Annual variation Year07 Year08 Year09 Year10 Year11

0.043 0.020 0.010 0.010 0.067

10.93 3.87 1.59 2.09 7.19

0.000 0.000 0.112 0.036 0.000

0.028 0.033 0.030 0.014 0.016

8.42 7.39 4.87 2.86 1.99

0.000 0.000 0.000 0.004 0.047

Contrac specific variables Moneyness Maturity Exp_week Exp_month Quarter Winter

0.025 0.056 0.164 0.054 0.106 0.029

1.61 10.04 4.86 7.50 22.81 3.50

0.108 0.000 0.000 0.000 0.000 0.001

0.027 0.059 0.025 0.049 0.107 0.001

2.08 14.08 0.94 7.89 24.95 0.08

0.037 0.000 0.346 0.000 0.000 0.939

Adj. R sqr. F - value p - value

0.55 97.94 0.000

0.59 95.6 0.000

6. Conclusions Seasonality refers to a phenomenon in which return, volatility, and trading volume time series fluctuate seasonally. This paper examined seasonalities in trading activity of the NASDAQ OMX electricity options. It accessed intraday data on all recorded option trades in the NASDAQ OMX Commodities Europe financial market in the period January, 2006–September, 2011 to examine whether trading volumes, trade sizes, and trading probabilities exhibit market specific seasonal patterns. In the world's largest and most liquid financial market for financial derivatives on electricity, the options are primarily used in hedging against quantity and price risks encountered in the physical market by both electricity producers, that is, electricity companies and their trading entities, and by users of electricity. In addition, electricity is non-storable, which also makes the market different from other financial markets and most other commodity markets. We presented four testable hypotheses on seasonal trading behavior, which are specific to the electricity options market. We find that 10

J. Nikkinen, T. Rothovius

Journal of Commodity Markets xxx (2018) 1–14

Table 5 Seasonality in trading volume in euros, excluding years 2008 and 2009. The following linear regression models are estimated: gm ¼ Wαm þ εm , where gm is a ðn  1Þ vector of ln of trading volume in euros, W is a ðn  32Þ design matrix of explanatory variables and αm is a ð32  1Þ vector of parameters to be estimated and εm a ðn  1Þ vector of random errors. The basic set of explanatory seasonal variables is defined as previously in model (1). In addition, six option contract specific variables are defined. These are moneyness, maturity, expiration week, expiration month, underlying type, and expiration cycle. Option moneyness is measured using the delta of an option. The maturity of an option is time-to-eqxpiration expressed in years, expiration week and expiration month are dummies indicating one week and one month before the expiration date respectively, and quarter is a dummy variable having the value 1 if the underlying is a quarterly futures contract and otherwise zero. Winter is a dummy variable having the value 1 if the underlying futures contract expires during the first quarter of the year and otherwise zero. The White heteroscedasticity consistent covariance matrix is used. Call options

Put Options

Es.

t-value

p-value

Es.

t-value

p-value

Intercept

1.667

9.23

0.000

1.545

9.39

0.000

Monthly variation Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

0.552 0.672 0.764 0.751 0.662 0.471 0.586 0.864 0.835 0.604 0.487

3.50 4.26 4.93 4.63 4.10 2.73 3.36 5.32 4.79 3.67 2.92

0.001 0.000 0.000 0.000 0.000 0.006 0.001 0.000 0.000 0.000 0.004

0.344 0.128 0.164 0.249 0.407 0.316 0.341 0.701 0.414 0.000 0.075

2.26 0.67 1.07 1.60 2.89 2.06 2.22 4.98 2.50 0.00 0.52

0.024 0.504 0.284 0.109 0.004 0.039 0.026 0.000 0.013 1.000 0.604

Day-of-the-week effect Mon Tue Wed Thu

0.118 0.093 0.061 0.169

1.48 1.52 1.05 2.72

0.140 0.129 0.296 0.007

0.027 0.207 0.048 0.048

0.28 2.86 0.61 0.59

0.781 0.004 0.543 0.556

Intraday variation 8–9 9–10 10–11 12–13 13–14 14–15 15–16

0.026 0.088 0.038 0.034 0.109 0.171 0.311

0.24 1.11 0.53 0.46 1.43 2.54 3.62

0.810 0.268 0.595 0.648 0.152 0.011 0.000

0.155 0.225 0.123 0.027 0.006 0.169 0.307

1.18 2.55 1.54 0.33 0.08 2.27 3.02

0.238 0.011 0.124 0.743 0.937 0.023 0.003

Annual variation Year07 Year10 Year11

0.114 0.240 0.177

2.35 4.30 2.34

0.019 0.000 0.019

0.353 0.242 0.058

6.61 3.03 0.56

0.000 0.003 0.575

Contract specific variables Quarter Winter Maturity Exp_week Exp_month Moneyness

0.197 0.671 0.506 0.943 0.571 4.197

3.09 8.38 5.59 5.95 7.43 26.09

0.002 0.000 0.000 0.000 0.000 0.000

0.659 0.868 0.978 2.146 0.636 5.138

8.77 8.88 11.04 4.22 6.37 18.07

0.000 0.000 0.000 0.000 0.000 0.000

Adj. R sqr. F – value p – value

0.49 59.14 0.000

0.48 45.46 0.000

the electricity options market differs from other financial markets in many respects. First, options on quarterly futures contracts are more heavily traded than options on yearly contracts. This may be because quarterly contracts provide the more flexible tool for hedging. Second, trading activity is higher for the winter months, since the prices are more volatile during that period and the peak prices are concentrated in these months. Third, trading activity is not greater prior to the expiration of the option. This implies that the contracts are initiated early and not closed out prior to expiration, but they are exercised. Finally, trading activity does not decrease during the summer months. This is because hedging increases gradually and with increasing speed during the year. Our results offer a step toward a better understanding of the unique nature of commodities options markets in general, and more specifically electricity option markets. This is important for market participants hedging their positions, since understanding the market is crucial for utilizing the hedging opportunities in the most efficient way. Our analysis is for a single, though important, market in the cold climate and volatile market environment, giving room for further research on other big electricity or commodity option markets in 11

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Journal of Commodity Markets xxx (2018) 1–14

Table 6 Probability of trading. Seasonality in hourly trading probability is shown in Panel A for calls and in Panel B for puts. The following probability model is estimated: PrðtradeÞ ¼ Φðx0i βÞ, i ¼ 1; 2; :::; T, where PrðtradeÞ represents a probability that a trade occurs within a trading hour and, and xi is a ð1  26Þ vector of attributes, which are Intercept, month dummy variables (11), weekday dummy variables (4), trading hour dummy variables (7), and year dummies (5). β is a parameter vector and Φð⋅Þ is a cumulative standard normal distribution function. The following Poisson model is estimated for the hourly number of trades: eλi λyi i Prð# of trade ¼ yi Þ ¼ , i ¼ 1; 2; :::; T, yi ¼ 0, 1, 2, …, ln yi ¼ γ0 xi , where yi is the number of trades occurring at the ith trading hour, and γ is the yi ! parameter vector. Panel A. Call options No of observations (trading hours) Hourly trading probability Average number of trades per hour Max number of trades per hour

8386.00 19.27 0.32 12.00

Probit regression

Poisson regression

Variable Intercept

Est. 0.849

t-value 9.16

p-value 0.000

Est. 1.131

Chi sq. 96.05

p-value 0.000

Monthly variation Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

0.258 0.248 0.109 0.242 0.129 0.156 0.146 0.156 0.147 0.197 0.275

2.98 2.79 1.19 2.64 1.41 1.71 1.52 1.74 1.62 2.20 3.09

0.003 0.005 0.234 0.008 0.159 0.087 0.130 0.082 0.105 0.028 0.002

0.427 0.272 0.242 0.319 0.298 0.268 0.156 0.261 0.234 0.327 0.422

15.60 5.79 4.68 7.69 6.82 5.45 1.62 5.32 4.17 8.65 14.78

0.000 0.016 0.030 0.006 0.009 0.020 0.203 0.021 0.041 0.003 0.000

Day-of-the-week effect Mon Tue Wed Thu

0.177 0.010 0.047 0.033

3.19 0.20 0.94 0.66

0.001 0.843 0.350 0.510

0.209 0.016 0.074 0.028

9.36 0.07 1.53 0.21

0.002 0.972 0.216 0.643

Intraday variation 08–0900 09–1000 10–1100 12–1300 13–1400 14–1500 15–1600

0.792 0.095 0.120 0.080 0.093 0.231 0.246

9.88 1.48 1.92 1.24 1.49 3.76 4.00

0.000 0.140 0.055 0.216 0.137 0.000 0.000

1.482 0.175 0.224 0.186 0.095 0.323 0.339

134.15 4.62 9.23 5.18 1.57 20.02 22.12

0.000 0.031 0.002 0.023 0.210 0.000 0.000

Annual variation Year07 Year08 Year09 Year10 Year11

0.092 0.258 0.332 0.279 0.425

1.93 4.96 6.15 5.18 6.39

0.053 0.000 0.000 0.000 0.000

0.103 0.370 0.560 0.499 0.881

3.75 36.79 78.79 57.98 91.02

0.053 0.000 0.000 0.000 0.000

McFadden's McKelvey-Zavoina

LRI

0.05 0.11

Panel B. Put options No of observations (trading hours) Hourly trading probability Average number of trades per hour Max number of trades per hour

8386.00 16.55 0.26 8.00

Probit regression

Poisson regression

Variable Intercept

Est. 0.797

t-value 8.51

p-value 0.000

Est. 0.912

Chi sq. 62.94

p-value 0.000

Monthly variation Jan

0.162

1.85

0.064

0.141

1.76

0.185

(continued on next page) 12

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Table 6 (continued ) Feb Mar Apr May Jun Jul Aug Sep Oct Nov

0.152 0.017 0.053 0.108 0.037 0.113 0.211 0.015 0.038 0.061

1.62 0.19 0.56 1.18 0.40 1.13 2.37 0.17 0.43 0.68

0.105 0.847 0.572 0.238 0.691 0.257 0.018 0.867 0.670 0.497

0.267 0.123 0.044 0.122 0.185 0.290 0.271 0.085 0.119 0.048

5.04 1.20 0.14 1.21 2.42 5.15 6.59 0.55 1.12 0.18

0.025 0.274 0.706 0.271 0.119 0.023 0.010 0.457 0.290 0.668

Day-of-the-week effect Mon Tue Wed Thu

0.250 0.066 0.120 0.023

4.19 1.24 2.31 0.42

0.000 0.216 0.021 0.672

0.412 0.114 0.110 0.019

26.60 2.98 2.86 0.08

0.000 0.085 0.091 0.780

Intraday variation 08–0900 09–1000 10–1100 12–1300 13–1400 14–1500 15–1600

0.715 0.175 0.122 0.024 0.136 0.283 0.216

8.57 2.52 1.86 0.35 2.08 4.40 3.33

0.000 0.012 0.062 0.725 0.038 0.000 0.001

1.340 0.372 0.299 0.067 0.079 0.353 0.351

103.36 15.10 13.69 0.63 0.87 19.53 19.27

0.000 0.000 0.000 0.428 0.351 0.000 0.000

Annual variation Year07 Year08 Year09 Year10 Year11

0.075 0.258 0.375 0.528 0.784

1.55 4.86 6.75 9.02 10.09

0.122 0.000 0.000 0.000 0.000

0.158 0.351 0.680 1.057 1.520

7.82 30.44 88.05 155.79 146.49

0.005 0.000 0.000 0.000 0.000

McFadden's McKelvey-Zavoina

LRI

0.06 0.15

different environments where, for example, the peak energy demand may occur during the summer time. The various roles of different kinds of traders, such as hedgers or speculators or liquidity providers, would also be an important area of subsequent research. Since the market is used for hedging purposes in the first place, and market participants are more or less forced into hedging their positions, it is important that the market is as efficient as possible. Nevertheless, as our results evidence, the market is very thinly traded, which suggests that efficiency could be improved by increasing trading. This could be done by attracting more speculative traders, and also small hedgers, to enter the market, but even more importantly, applying a market-making regime to reduce the bid-ask spread and ensuring a trade whenever needed by a hedger. This would be most important for the contracts hedging the most volatile times. Market making could therefore be provided at least for those contracts and/or certain specific periods. The results of our study may help to identify such option contracts and periods. Finally, a central question is what kind of benefits market participants, especially hedgers, might gain from the more regulated intermediation sector and how great a benefit is feasible. Acknowledgements We would like to thank the participants of the 30th French Finance Association AFFI meeting, and two anonymous referees for their valuable comments. The generous financial support from the Nasdaq OMX Nordic foundation is gratefully acknowledged. Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jcomm.2018.05.002. References Abhyankar, A., Ghosh, D., Levin, E., Limmack, R.J., 1997. Bid-Ask spreads, trading volume and volatility: intra-day evidence from the London Stock Exchange. J. Bus. Finance Account. 24, 343–362. Aggarwal, R., Rivoli, P., 1989. Seasonal and day-of-the-week effect in four emerging stock markets. Financ. Rev. 24, 541–550. Amemiya, T., 1986. Advanced Econometrics. MA. Harvard University Press, Cambridge. Back, J., Prokopczuk, M., Rudolf, M., 2013. Seasonality and the valuation of commodity options. J. Bank. Finance 37, 273–290. Benth, F.E., Biegler-K€ onig, R., Kiesel, R., 2013. An empirical study of the information premium on electricity markets. Energy Econ. 36, 55–77. Birkelund, O., Haugom, E., Molnar, P., Opdal, M., Westgaard, S., 2015. A comparison of implied and realized volatility in the Nordic power forward market. Energy Econ. 48, 288–294. 13

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