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Pricing IMF liquidity provision
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Emerging Markets Review 9 (2008) 70 – 77 www.elsevier.com/locate/emr
Pricing IMF liquidity provision ☆ The value of the IMF liquidity commitment Marco Rossi ⁎ International Monetary Fund, 700 19th Street NW, Washington DC 20431, United States Received 12 June 2007; received in revised form 15 November 2007; accepted 2 December 2007 Available online 8 December 2007
Abstract This paper presents a market-based framework for pricing the International Monetary Fund's commitment to provide liquidity assistance, accounting for the credit risk and the insurance benefit involved in such operations. It is based on the isomorphic correspondence between Fund liquidity and common stock put options. The illustrative numerical examples show that the value of this liquidity guarantee could range between several and three hundreds basis points depending on the borrower's creditworthiness, the volatility of capital flows to the borrowing country, and the amount of funds potentially needed to meet the borrower's external obligations. © 2007 International Monetary Fund. Published by Elsevier B.V. JEL classification: F33; F34; F53; G13 Keywords: IMF financing facility; Lender of last resort; Liquidity provision; Option pricing
1. Introduction Lending from the International Monetary Fund (IMF) has traditionally aimed at supporting members' balance of payments, and, increasingly since the Mexican crisis, it has responded to the need to provide financial assistance to members experiencing exceptional pressures on their capital account (and reserves) as a result of a sudden and disruptive loss of market confidence. Since the crises in South-East Asia and other emerging market economies, the design of a liquidity instrument that could help prevent financial crises has featured prominently on the IMF's reform agenda. Such ☆ The views expressed in this paper are those of the author and do not necessarily represent those of the IMF or IMF policy. The author would like to thank Gabriele Zinna and the anonymous referee for helpful comments. The usual disclaimer applies. ⁎ Corresponding author. Tel.: +1 202 6235651; fax: +1 202 5895651. E-mail address: [email protected].
1566-0141/$ - see front matter © 2007 International Monetary Fund. Published by Elsevier B.V. doi:10.1016/j.ememar.2007.12.002
M. Rossi / Emerging Markets Review 9 (2008) 70–77
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an instrument was deemed to complement the existing borrowing toolkit available to the membership, which had been expanded in the late 1990s with the introduction of the Supplemental Reserve Facility,1 but whose aim remained that of resolving – rather than preventing – financial crisis. A first attempt at introducing a contingent liquidity instrument for countries with access to capital markets–namely, the creation of the Contingent Credit Line (CCL) facility — did not meet with enough interest from the membership and the facility was let to expire.2 Many have continued to call for a new IMF financing instrument specifically designed to support crisis prevention in countries with access to international capital markets.3 And the IMF Medium-Term Strategy underscores the need to make further progress on designing such a liquidity instrument that could muster the support of the membership.4 The discussion continues.5 Since crisis prevention is the nature of the new liquidity instrument under discussion, its design should meet two key criteria for the user. First, liquidity should be available with a high degree of automaticity and reliability. Second, the cost of the instrument should reflect its benefit in preventing a crisis; prospective users would probably compare this cost with that of alternative ways to insure against a possible crisis. For the liquidity provider, an additional criterion is key: containing financial risks and safeguarding its resources. Clearly, a series of design elements – pricing, access, qualification, monitoring, maturity structure, length of time during which liquidity through the new instrument is available – will impinge upon the attractiveness of the new liquidity instrument and will probably be considered as a package. This paper focuses on pricing. At this stage of the discussion on the new liquidity instrument, it is envisaged that borrowers will be assessed, as customary, the rate of charge on IMF loans plus level- and time-based surcharges, and commitment and service fees.6 While these charges and fees are intended to recoup funding, administrative and opportunity costs and to build precautionary balances, they do not explicitly incorporate an assessment of the borrower's credit risk, and the intrinsic value of the liquidity guarantee that it provides to the borrower.7 It is this latter prominent feature of a new contingent liquidity facility the specific focus of this paper. This paper proposes a market-based framework for pricing the value of an IMF's commitment to provide liquidity that explicitly distinguishes between lower- and higher-risk borrowers, while incorporating the benefits to the borrower of being able to tap a source of liquidity when necessary. The framework is based on the isomorphic correspondence between IMF liquidity and common stock put options, and is consistent with the literature on modern portfolio insurance (Black and Jones, 1987). The fees generated by this framework would be assessed upfront at time of qualification to reflect IMF's contingent commitment to provide liquidity. Potential users could compare these with the costs of alternative insurance strategies. 1
Press Release No. 97/59, December 17, 1997 (http://www.imf.org/external/np/sec/pr/1997/pr9759.htm). Press Release No. 03/207, November 26, 2003 (http://www.imf.org/external/np/sec/pr/2003/pr03207.htm). 3 Most recently, see “Is the IMF Obsolete”, The International Economy, Spring 2007. 4 A Medium-Term Strategy for the IMF: Meeting the Challenge of Globalization http://www.imf.org/external/np/exr/ib/ 2006/041806.htm. 5 Public Information Notice No. 07/40, March 23, 2007 (http://www.imf.org/external/np/sec/pn/2007/pn0740.htm). 6 Further Consideration of a New Liquidity Instrument for Market Access Countries—Design Issues, February 13, 2007 (www.imf.org). See http://www.imf.org/external/np/tre/sdr/burden/2007/082007.htm for a detailed explanation of the rate of charge. 7 The Fund's preferred creditor status is often mentioned to weaken the rationale for formally assessing credit risk. However, pricing such a risk would help restore a proper ex ante incentive structure to borrow and foster the implementation of policies that would minimize the chances of having to receive Fund financing assistance. 2
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2. Pricing IMF liquidity commitment under a contingent liquidity instrument As noted, by qualifying for contingent IMF liquidity a country would purchase the right to borrow from the IMF in case of need. The IMF, in turn, would charge a commitment fee upfront equal to the value of the insurance to the potential borrower. In case the borrower eventually requires IMF financial assistance, it will be charged the customary rate of charge plus applicable surcharges and service fee on the amount effectively drawn, while the commitment fee would be refunded. 2.1. The conceptual framework A member country seeks to qualify for access to IMF liquidity, which is extended for, say, a year. At the time of qualification, the amount of the country's net external obligations, (D), over the following year–net short-term debt by residual maturity–is known.8 These obligations can be met by using the country's stock of international reserves (R) and/or accessing the international capital markets (MA), in the form of syndicated loans and/or Eurobond placements. A country's liquidity position (L) can therefore be defined as: L ¼ R þ MA
ð1Þ
whose level and fluctuations depend on the behavior of R and MA over time. The level of a country's reserves is affected by the flows in its balance of payments as well as changes in its residents' currency preferences, which are both stochastic. This is consistent with the buffer stock model – Frenkel and Jovanovic (1981) – predicating that the optimal holdings of reserves depends on the variability of international transactions.9 According to this framework, R can be described by a geometric Brownian motion: dR ¼ cRdt þ rRdz
ð2Þ
where dz is a Wiener process, implying a log-normal distribution for R. Access to capital markets depends on the country's perceived ability to continue meeting its obligations. Such a market perception may not always reflect fundamentals–the level of D for instance–as shown during episodes of financial turbulence over the past decade. The determination of many countries to insulate themselves from contagion underpins the interest in contingent liquidity instruments. At any point in time, a country then may or may not be able to rely on market financing to complement its international reserve position to service its obligations. MA can therefore be described by a stationary binomial stochastic process: MA ¼ ð>0; with probability q; 0; with probability 1 qÞ
ð3Þ
with q is the probability of being liquid.
8
Clearly a country's liquidity requirements may exceed its net short-term debt in a crisis situation when capital flight is likely. D would then need to be defined in practice on a case-by-case basis, including by taking the country's financial structure and degree of dollarization into account. 9 For en empirical analysis of the buffer stock model see Flood and Marion (2002), which uses a panel data approach, and Silva and da Silva (2004), which uses a time-series analysis and discusses specific country features. See also Salman and Salih (1999) and Ramachandran (2004) for applications to Turkey and India, respectively.
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By qualifying for IMF liquidity, a member would be able to obtain additional liquidity – that is, in addition to its current level of reserves – in the case of a reversal of market sentiments – i.e. MA = 0 – at any time over the lifespan of the instrument. The value of this liquidity guarantee to the member is: V ¼ f0 with probability q maxð D R; 0Þ with probability ð1 qÞg
ð4Þ
The second term in Eq. (4) is akin to the payoff of a put option, where the amount of international reserves, R, is the stock price and the amount of debt service, D, is the strike price. By qualifying a member country for access to liquidity, the IMF would be writing a (notional) put option on the member's liquidity. By exercising the option, the member country would obtain a cash inflow in the case its liquidity falls short of its short-term obligations, that is, in a situation in which other sources of external borrowing cannot be accessed. 2.2. The operational framework From an operational viewpoint, pricing IMF liquidity would entail pricing the put option and assessing the probability of no access to capital markets for a qualifying member country. Pricing this liquidity guarantee, we would have: EQ ½V ¼ E EQ ½V jMA
ð5Þ
And applying the tower property: EQ ½V ¼ EQ f½V jMAN0T Pr½MAN0g þ EQ f½V jMA ¼ 0T Pr½MA ¼ 0g ¼ EQ f½maxð D R; 0ÞjMA ¼ 0T ð1 qÞg
ð6Þ
where Q is the risk neutral probability. While a country's liquidity requirements – as proxied by the level of its short-term debt – are likely to affect its access to capital markets, the likelihood that MA = 0 at some point in time hinges on an overall assessment of a wider set of economic, financial, and political indicators, and ultimately on a judgment of the consistency, including in the short term, of a country's economic policy mix. In this context, Eq. (6) collapses to: EQ ½V ¼ EQ f½maxð D R; 0ÞTð1 qÞg
ð7Þ
2.2.1. Pricing the put option Calculating the option premium depends on the type of option being written. Access to IMF liquidity could be allowed (i) once to coincide with its expiration, (ii) a discrete number of times, or (iii) at any point in time. The option would, respectively, be a European, Bermudan, or American and its valuation present increasing complexity.10
10
A premium is attached to the privilege of early exercise provided by Bermudan and American options, which is reflected in the value of a European option being not greater than those of the other types.
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2.2.2. European option The value of the put option or the cost of the liquidity guarantee, according to the Black and Scholes formula (Black and Scholes, 1973), would be: V ðsÞ ¼ ð1 qÞ½Ders N ðd2 Þ RN ðd1 Þ
ð5aÞ
where: 1 D r2 d1 ¼ pffiffiffi ln r þ s R 2 r s pffiffiffi d2 ¼ d1 þ r s σ2 r τ N(di)
is is is is
the the the the
variance rate per unit of time for the logarithmic change in the value of R discount factor maturity of the option contract cumulative normal density function.
Per unit of external obligations, D, this could be expressed as: vðsÞ ¼ ð1 qÞ½N ðx2 Þ 1=dN ðx1 Þ
ð5bÞ
where:
1 x1 ¼ pffiffiffi lnd r2 s r s pffiffiffi x2 ¼ x 1 þ r s σ2 τ
is the variance of the logarithmic change in the value of R during the term of the IMF facility
d¼
Ders R
2.2.3. Bermudan and American options No exact pricing formula, like Black–Scholes', exists; numerical procedures and analytic approximations are instead used. These include the binomial option pricing model and finite difference methods. Software is available to calculate option prices on the basis of these numerical and analytic methodologies. 2.3. Assessing the probability of no access to markets An assessment of a member country's probability to have access to international capital markets seriously curtailed at some point in time can be proxied by a number of indicators: early warning systems, ratings transition matrices, implied probability of default embedded in derivative assets prices–credit default swaps, currency and sovereign debt options, for instance–
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Table 1 Sovereign transition risk-neutral probabilities To: From: Aaa Aa A Baa Ba B C Default
Aaa
(In Percent) 0.96 0.05 0.00 0.00 0.00 0.00 0.00 0.00
Aa
A
Baa
Ba
B
C
Default
0.02 0.92 0.03 0.00 0.00 0.00 0.00 0.00
0.00 0.01 0.91 0.08 0.00 0.00 0.00 0.00
0.00 0.00 0.02 0.85 0.06 0.00 0.00 0.00
0.00 0.00 0.00 0.03 0.82 0.04 0.01 0.00
0.00 0.00 0.00 0.00 0.06 0.84 0.20 0.00
0.00 0.00 0.00 0.00 0.00 0.05 0.67 0.00
0.02 0.03 0.03 0.03 0.05 0.07 0.12 1.00
Source: Rossi and Zinna (2007).
and financial indicators on financial risks and stability–such as the expected number of defaults, the distance to default. One or more of these proxies are usually available or could be constructed for each member country with access to international capital markets. Such an index would typically be a small number, reflecting the fact that IMF liquidity provision would be targeted to those countries that are vulnerable, but are implementing, at the time of qualification, sustainable policies. 2.4. Some illustrative numerical examples Below are some illustrative numerical examples to show how the framework could be used in practice. The process of calculating the value of the guarantee that the IMF would extend through providing liquidity is twofold. First, the probability of being illiquid – i.e., (1 − q) in Eq. (7) – for each borrower needs to be estimated. Rossi and Zinna (2007) estimate transition probabilities using the homogeneous hazard rate estimator on Moody's sovereign rating dataset spanning 1984–2007. Risk natural transition probabilities are derived for each class of sovereign. A numerical technique that adjusts the empirical transition matrix with market risk premia to recover risk neutral probabilities, which are needed for pricing purposes. Table 1, from Rossi and Zinna (2007), reports the one-year risk neutral transition probability matrix calibrated on August 14, 2007 on Euro-dollar bonds assuming a 70% recovery rate given default, which is in line with the evidence provided in Moody (2007). In the numerical examples below, (1 − q) is equal to 1.93% for a Aaa borrower, 2.68% for a Aa borrower, and so forth. Table 2 reports the value of the American put option embedded in the IMF liquidity provision for different values of a country's net external position-to-reserves ratio and the volatility of its Table 2 Value of put optiona For d = 0.7; σ2 = 10 For d = 0.7; σ2 = 30 For d = 0.8; σ2 = 10 For d = 0.8; σ2 = 30 For d = 1; σ2 = 10 For d = 1; σ2 = 30 a
In percentage points; τ is one year and r is the one-year US treasury bill rate.
40.0 40.1 20.0 22.7 2.4 9.9
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Table 3 Value of Fund liquiditya Type of borrower For d = 0.7; σ2 = 10 For d = 0.7; σ2 = 30 For d = 0.8; σ2 = 10 For d = 0.8; σ2 = 30 For d = 1; σ2 = 10 For d = 1; σ2 = 30 a
Aaa
Aa
A
Baa
Ba
B
0.77 0.77 0.39 0.44 0.05 0.19
1.07 1.07 0.54 0.61 0.07 0.26
1.18 1.19 0.59 0.67 0.07 0.29
1.37 1.37 0.68 0.78 0.08 0.34
1.88 1.89 0.94 1.07 0.11 0.46
2.98 2.99 1.49 1.69 0.18 0.74
In percentage points; τ is one year and r is the one-year US treasury bill rate.
capital flows. The liquidity guarantee is assumed to be issued for one year, that is, the maturity of the option is one year. The risk-free discount factor is proxied by the one-year US treasury bill rate.11 Finally, Table 3 reports the value of the liquidity insurance provided by the IMF in case of a reversal in market sentiments. It ranges from several to almost three hundreds basis points, reflecting the borrower's credit and liquidity risks as well as its debt to reserves ratio. As expected, the value of the guarantee increases with the reserves-to-debt ratio, reserves volatility, while decreases with a country's ratings. For instance, the value of IMF liquidity for a Baa-rated country with about 80 percent of its short-term debt by remaining maturity covered by reserves and capital flow volatility of about 10 percent would be about 70 basis points to be assessed at time of qualification. The value of the guarantee is not reported for borrowers in the C categories as these would not qualify for access to IMF contingent liquidity. For countries with large obligations compared to available resources (small dl), the value of the guarantee is not affected by the volatility of its resources in any significant way as the put option is heavily in the money. 3. Conclusion Although not formally enshrined in its articles of agreement, the IMF has often operated as the ultimate provider of international liquidity, most notably in the more recent capital account crises, to deal with an exceptional situation that posed a threat to the stability of the international monetary system. This paper presents a market-based framework for pricing IMF commitment to provide contingent liquidity assistance that accounts for the credit risk and the insurance involved in such operations. It underscores the benefits to the member country of being able to access liquidity when needed. The framework is based on the isomorphic correspondence between IMF liquidity and common stock put options. As a market-based framework, it provides the necessary economic incentives to the prospective borrower, while explicitly assessing the costs for the liquidity provider. Market-signaling issues would need to be dealt with, given that the principle of equality of treatment across the membership is central to the IMF's mandate. However, and while assuming that the IMF should not differentiate risk across its membership, it is worth noting that asset prices may already fully reflect the risk assessment of a specific borrower in orderly functioning markets, which 11 The American put option is used in the simulation as it is the one that would most closely fit a situation in which, after qualification, a member could access Fund liquidity at any time over the lifespan of the instrument. This is indeed the setting under the current proposal for a new liquidity instrument.
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would be the case at the time a member is qualified for access to contingent IMF liquidity. The distinction between lower- and higher-risks would thus reflect public market information. Moreover, the case that the potential differentiation across members would still be consistent with the principle of equality of treatment could be argued on the basis that countries in the same conditions would be assessed the same fee. Finally, the fact that the probability of default is estimated for rating categories, rather than for individual borrowers, may also allay signaling concerns. These signaling concerns need not being overemphasized as, in practice, differences in prices potentially assessed to borrowers according to this approach may not be that significant as the qualification requirement would tend to select a relatively homogenous set of countries. Also, the use of summary indices to assess a member's probability of being illiquid could, in practice, blur differences across the membership. Finally, from a technical viewpoint, the put option is likely to be heavily in the money for the majority of the countries that would have an interest in qualifying for access to contingent IMF liquidity, reflecting large obligations compared to available resources. A country's risk, as assessed by the volatility of its resources, would then have a negligible impact on the value of the put option, evening out the premiums across countries. The numerical examples presented in this paper are only illustrative. They show that the value of the liquidity guarantee provided by accessing IMF liquidity could range from several to almost three hundreds basis points depending on the borrower's creditworthiness, the volatility of capital flows to the borrowing country, and the amount of funds that would be potentially needed to meet the borrower's external obligations. The cost of this liquidity guarantee, which incorporates both credit risk and the instrument's insurance value, would be assessed as a commitment fee upfront. This fee could be refunded in case IMF resources are effectively drawn as per current practices, at which point the charges associated with existing IMF facilities would apply. The level of these commitment fees would need to be evaluated against other design elements of the new liquidity instrument. In practice, there is likely a trade-off between cost and automaticity in accessing liquidity, and different users may aim at a different trade-off. References Black, F., Jones, R., 1987. Simplifying portfolio insurance. Journal of Portfolio Management, Fall 48–51 (Institutional Investor). Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654 (University of Chicago Press). Flood, R., Marion, N., 2002. Holding International Reserves in an Era of High Capital Mobility. IMF working paper No. WP/02/62. Frenkel, J., Jovanovic, B., 1981. Optimal International Reserves: A Stochastic Framework. Economic Journal 91, 507–514. Moody's Investor Service, Sovereign Default and Recovery Rates, 1983–2006, Special Comment June 2007. Ramachandran, M., 2004. The optimal level of international reserves: evidence for India. Economics Letters 83, 365–370 (Elsevier BV, North-Holland). Rossi, M., Zinna, G., 2007. Sovereign Credit Risk: A Rating-Based Perspective. International Monetary Fund, mimeo. Salman, F., Salih, A., 1999. Modeling the volatility in the Central Bank reserves. Research Paper of Central Bank of Turkey. Silva, A.F., da Silva, E., 2004. Optimal international reserves holdings in emerging markets economies: the Brazilian case. www.anpec.org.br/encontro2004/artigos/A04A078.pdf.
Emerging Markets Review 9 (2008) 70 – 77 www.elsevier.com/locate/emr
Pricing IMF liquidity provision ☆ The value of the IMF liquidity commitment Marco Rossi ⁎ International Monetary Fund, 700 19th Street NW, Washington DC 20431, United States Received 12 June 2007; received in revised form 15 November 2007; accepted 2 December 2007 Available online 8 December 2007
Abstract This paper presents a market-based framework for pricing the International Monetary Fund's commitment to provide liquidity assistance, accounting for the credit risk and the insurance benefit involved in such operations. It is based on the isomorphic correspondence between Fund liquidity and common stock put options. The illustrative numerical examples show that the value of this liquidity guarantee could range between several and three hundreds basis points depending on the borrower's creditworthiness, the volatility of capital flows to the borrowing country, and the amount of funds potentially needed to meet the borrower's external obligations. © 2007 International Monetary Fund. Published by Elsevier B.V. JEL classification: F33; F34; F53; G13 Keywords: IMF financing facility; Lender of last resort; Liquidity provision; Option pricing
1. Introduction Lending from the International Monetary Fund (IMF) has traditionally aimed at supporting members' balance of payments, and, increasingly since the Mexican crisis, it has responded to the need to provide financial assistance to members experiencing exceptional pressures on their capital account (and reserves) as a result of a sudden and disruptive loss of market confidence. Since the crises in South-East Asia and other emerging market economies, the design of a liquidity instrument that could help prevent financial crises has featured prominently on the IMF's reform agenda. Such ☆ The views expressed in this paper are those of the author and do not necessarily represent those of the IMF or IMF policy. The author would like to thank Gabriele Zinna and the anonymous referee for helpful comments. The usual disclaimer applies. ⁎ Corresponding author. Tel.: +1 202 6235651; fax: +1 202 5895651. E-mail address: [email protected].
1566-0141/$ - see front matter © 2007 International Monetary Fund. Published by Elsevier B.V. doi:10.1016/j.ememar.2007.12.002
M. Rossi / Emerging Markets Review 9 (2008) 70–77
71
an instrument was deemed to complement the existing borrowing toolkit available to the membership, which had been expanded in the late 1990s with the introduction of the Supplemental Reserve Facility,1 but whose aim remained that of resolving – rather than preventing – financial crisis. A first attempt at introducing a contingent liquidity instrument for countries with access to capital markets–namely, the creation of the Contingent Credit Line (CCL) facility — did not meet with enough interest from the membership and the facility was let to expire.2 Many have continued to call for a new IMF financing instrument specifically designed to support crisis prevention in countries with access to international capital markets.3 And the IMF Medium-Term Strategy underscores the need to make further progress on designing such a liquidity instrument that could muster the support of the membership.4 The discussion continues.5 Since crisis prevention is the nature of the new liquidity instrument under discussion, its design should meet two key criteria for the user. First, liquidity should be available with a high degree of automaticity and reliability. Second, the cost of the instrument should reflect its benefit in preventing a crisis; prospective users would probably compare this cost with that of alternative ways to insure against a possible crisis. For the liquidity provider, an additional criterion is key: containing financial risks and safeguarding its resources. Clearly, a series of design elements – pricing, access, qualification, monitoring, maturity structure, length of time during which liquidity through the new instrument is available – will impinge upon the attractiveness of the new liquidity instrument and will probably be considered as a package. This paper focuses on pricing. At this stage of the discussion on the new liquidity instrument, it is envisaged that borrowers will be assessed, as customary, the rate of charge on IMF loans plus level- and time-based surcharges, and commitment and service fees.6 While these charges and fees are intended to recoup funding, administrative and opportunity costs and to build precautionary balances, they do not explicitly incorporate an assessment of the borrower's credit risk, and the intrinsic value of the liquidity guarantee that it provides to the borrower.7 It is this latter prominent feature of a new contingent liquidity facility the specific focus of this paper. This paper proposes a market-based framework for pricing the value of an IMF's commitment to provide liquidity that explicitly distinguishes between lower- and higher-risk borrowers, while incorporating the benefits to the borrower of being able to tap a source of liquidity when necessary. The framework is based on the isomorphic correspondence between IMF liquidity and common stock put options, and is consistent with the literature on modern portfolio insurance (Black and Jones, 1987). The fees generated by this framework would be assessed upfront at time of qualification to reflect IMF's contingent commitment to provide liquidity. Potential users could compare these with the costs of alternative insurance strategies. 1
Press Release No. 97/59, December 17, 1997 (http://www.imf.org/external/np/sec/pr/1997/pr9759.htm). Press Release No. 03/207, November 26, 2003 (http://www.imf.org/external/np/sec/pr/2003/pr03207.htm). 3 Most recently, see “Is the IMF Obsolete”, The International Economy, Spring 2007. 4 A Medium-Term Strategy for the IMF: Meeting the Challenge of Globalization http://www.imf.org/external/np/exr/ib/ 2006/041806.htm. 5 Public Information Notice No. 07/40, March 23, 2007 (http://www.imf.org/external/np/sec/pn/2007/pn0740.htm). 6 Further Consideration of a New Liquidity Instrument for Market Access Countries—Design Issues, February 13, 2007 (www.imf.org). See http://www.imf.org/external/np/tre/sdr/burden/2007/082007.htm for a detailed explanation of the rate of charge. 7 The Fund's preferred creditor status is often mentioned to weaken the rationale for formally assessing credit risk. However, pricing such a risk would help restore a proper ex ante incentive structure to borrow and foster the implementation of policies that would minimize the chances of having to receive Fund financing assistance. 2
72
M. Rossi / Emerging Markets Review 9 (2008) 70–77
2. Pricing IMF liquidity commitment under a contingent liquidity instrument As noted, by qualifying for contingent IMF liquidity a country would purchase the right to borrow from the IMF in case of need. The IMF, in turn, would charge a commitment fee upfront equal to the value of the insurance to the potential borrower. In case the borrower eventually requires IMF financial assistance, it will be charged the customary rate of charge plus applicable surcharges and service fee on the amount effectively drawn, while the commitment fee would be refunded. 2.1. The conceptual framework A member country seeks to qualify for access to IMF liquidity, which is extended for, say, a year. At the time of qualification, the amount of the country's net external obligations, (D), over the following year–net short-term debt by residual maturity–is known.8 These obligations can be met by using the country's stock of international reserves (R) and/or accessing the international capital markets (MA), in the form of syndicated loans and/or Eurobond placements. A country's liquidity position (L) can therefore be defined as: L ¼ R þ MA
ð1Þ
whose level and fluctuations depend on the behavior of R and MA over time. The level of a country's reserves is affected by the flows in its balance of payments as well as changes in its residents' currency preferences, which are both stochastic. This is consistent with the buffer stock model – Frenkel and Jovanovic (1981) – predicating that the optimal holdings of reserves depends on the variability of international transactions.9 According to this framework, R can be described by a geometric Brownian motion: dR ¼ cRdt þ rRdz
ð2Þ
where dz is a Wiener process, implying a log-normal distribution for R. Access to capital markets depends on the country's perceived ability to continue meeting its obligations. Such a market perception may not always reflect fundamentals–the level of D for instance–as shown during episodes of financial turbulence over the past decade. The determination of many countries to insulate themselves from contagion underpins the interest in contingent liquidity instruments. At any point in time, a country then may or may not be able to rely on market financing to complement its international reserve position to service its obligations. MA can therefore be described by a stationary binomial stochastic process: MA ¼ ð>0; with probability q; 0; with probability 1 qÞ
ð3Þ
with q is the probability of being liquid.
8
Clearly a country's liquidity requirements may exceed its net short-term debt in a crisis situation when capital flight is likely. D would then need to be defined in practice on a case-by-case basis, including by taking the country's financial structure and degree of dollarization into account. 9 For en empirical analysis of the buffer stock model see Flood and Marion (2002), which uses a panel data approach, and Silva and da Silva (2004), which uses a time-series analysis and discusses specific country features. See also Salman and Salih (1999) and Ramachandran (2004) for applications to Turkey and India, respectively.
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By qualifying for IMF liquidity, a member would be able to obtain additional liquidity – that is, in addition to its current level of reserves – in the case of a reversal of market sentiments – i.e. MA = 0 – at any time over the lifespan of the instrument. The value of this liquidity guarantee to the member is: V ¼ f0 with probability q maxð D R; 0Þ with probability ð1 qÞg
ð4Þ
The second term in Eq. (4) is akin to the payoff of a put option, where the amount of international reserves, R, is the stock price and the amount of debt service, D, is the strike price. By qualifying a member country for access to liquidity, the IMF would be writing a (notional) put option on the member's liquidity. By exercising the option, the member country would obtain a cash inflow in the case its liquidity falls short of its short-term obligations, that is, in a situation in which other sources of external borrowing cannot be accessed. 2.2. The operational framework From an operational viewpoint, pricing IMF liquidity would entail pricing the put option and assessing the probability of no access to capital markets for a qualifying member country. Pricing this liquidity guarantee, we would have: EQ ½V ¼ E EQ ½V jMA
ð5Þ
And applying the tower property: EQ ½V ¼ EQ f½V jMAN0T Pr½MAN0g þ EQ f½V jMA ¼ 0T Pr½MA ¼ 0g ¼ EQ f½maxð D R; 0ÞjMA ¼ 0T ð1 qÞg
ð6Þ
where Q is the risk neutral probability. While a country's liquidity requirements – as proxied by the level of its short-term debt – are likely to affect its access to capital markets, the likelihood that MA = 0 at some point in time hinges on an overall assessment of a wider set of economic, financial, and political indicators, and ultimately on a judgment of the consistency, including in the short term, of a country's economic policy mix. In this context, Eq. (6) collapses to: EQ ½V ¼ EQ f½maxð D R; 0ÞTð1 qÞg
ð7Þ
2.2.1. Pricing the put option Calculating the option premium depends on the type of option being written. Access to IMF liquidity could be allowed (i) once to coincide with its expiration, (ii) a discrete number of times, or (iii) at any point in time. The option would, respectively, be a European, Bermudan, or American and its valuation present increasing complexity.10
10
A premium is attached to the privilege of early exercise provided by Bermudan and American options, which is reflected in the value of a European option being not greater than those of the other types.
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2.2.2. European option The value of the put option or the cost of the liquidity guarantee, according to the Black and Scholes formula (Black and Scholes, 1973), would be: V ðsÞ ¼ ð1 qÞ½Ders N ðd2 Þ RN ðd1 Þ
ð5aÞ
where: 1 D r2 d1 ¼ pffiffiffi ln r þ s R 2 r s pffiffiffi d2 ¼ d1 þ r s σ2 r τ N(di)
is is is is
the the the the
variance rate per unit of time for the logarithmic change in the value of R discount factor maturity of the option contract cumulative normal density function.
Per unit of external obligations, D, this could be expressed as: vðsÞ ¼ ð1 qÞ½N ðx2 Þ 1=dN ðx1 Þ
ð5bÞ
where:
1 x1 ¼ pffiffiffi lnd r2 s r s pffiffiffi x2 ¼ x 1 þ r s σ2 τ
is the variance of the logarithmic change in the value of R during the term of the IMF facility
d¼
Ders R
2.2.3. Bermudan and American options No exact pricing formula, like Black–Scholes', exists; numerical procedures and analytic approximations are instead used. These include the binomial option pricing model and finite difference methods. Software is available to calculate option prices on the basis of these numerical and analytic methodologies. 2.3. Assessing the probability of no access to markets An assessment of a member country's probability to have access to international capital markets seriously curtailed at some point in time can be proxied by a number of indicators: early warning systems, ratings transition matrices, implied probability of default embedded in derivative assets prices–credit default swaps, currency and sovereign debt options, for instance–
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Table 1 Sovereign transition risk-neutral probabilities To: From: Aaa Aa A Baa Ba B C Default
Aaa
(In Percent) 0.96 0.05 0.00 0.00 0.00 0.00 0.00 0.00
Aa
A
Baa
Ba
B
C
Default
0.02 0.92 0.03 0.00 0.00 0.00 0.00 0.00
0.00 0.01 0.91 0.08 0.00 0.00 0.00 0.00
0.00 0.00 0.02 0.85 0.06 0.00 0.00 0.00
0.00 0.00 0.00 0.03 0.82 0.04 0.01 0.00
0.00 0.00 0.00 0.00 0.06 0.84 0.20 0.00
0.00 0.00 0.00 0.00 0.00 0.05 0.67 0.00
0.02 0.03 0.03 0.03 0.05 0.07 0.12 1.00
Source: Rossi and Zinna (2007).
and financial indicators on financial risks and stability–such as the expected number of defaults, the distance to default. One or more of these proxies are usually available or could be constructed for each member country with access to international capital markets. Such an index would typically be a small number, reflecting the fact that IMF liquidity provision would be targeted to those countries that are vulnerable, but are implementing, at the time of qualification, sustainable policies. 2.4. Some illustrative numerical examples Below are some illustrative numerical examples to show how the framework could be used in practice. The process of calculating the value of the guarantee that the IMF would extend through providing liquidity is twofold. First, the probability of being illiquid – i.e., (1 − q) in Eq. (7) – for each borrower needs to be estimated. Rossi and Zinna (2007) estimate transition probabilities using the homogeneous hazard rate estimator on Moody's sovereign rating dataset spanning 1984–2007. Risk natural transition probabilities are derived for each class of sovereign. A numerical technique that adjusts the empirical transition matrix with market risk premia to recover risk neutral probabilities, which are needed for pricing purposes. Table 1, from Rossi and Zinna (2007), reports the one-year risk neutral transition probability matrix calibrated on August 14, 2007 on Euro-dollar bonds assuming a 70% recovery rate given default, which is in line with the evidence provided in Moody (2007). In the numerical examples below, (1 − q) is equal to 1.93% for a Aaa borrower, 2.68% for a Aa borrower, and so forth. Table 2 reports the value of the American put option embedded in the IMF liquidity provision for different values of a country's net external position-to-reserves ratio and the volatility of its Table 2 Value of put optiona For d = 0.7; σ2 = 10 For d = 0.7; σ2 = 30 For d = 0.8; σ2 = 10 For d = 0.8; σ2 = 30 For d = 1; σ2 = 10 For d = 1; σ2 = 30 a
In percentage points; τ is one year and r is the one-year US treasury bill rate.
40.0 40.1 20.0 22.7 2.4 9.9
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Table 3 Value of Fund liquiditya Type of borrower For d = 0.7; σ2 = 10 For d = 0.7; σ2 = 30 For d = 0.8; σ2 = 10 For d = 0.8; σ2 = 30 For d = 1; σ2 = 10 For d = 1; σ2 = 30 a
Aaa
Aa
A
Baa
Ba
B
0.77 0.77 0.39 0.44 0.05 0.19
1.07 1.07 0.54 0.61 0.07 0.26
1.18 1.19 0.59 0.67 0.07 0.29
1.37 1.37 0.68 0.78 0.08 0.34
1.88 1.89 0.94 1.07 0.11 0.46
2.98 2.99 1.49 1.69 0.18 0.74
In percentage points; τ is one year and r is the one-year US treasury bill rate.
capital flows. The liquidity guarantee is assumed to be issued for one year, that is, the maturity of the option is one year. The risk-free discount factor is proxied by the one-year US treasury bill rate.11 Finally, Table 3 reports the value of the liquidity insurance provided by the IMF in case of a reversal in market sentiments. It ranges from several to almost three hundreds basis points, reflecting the borrower's credit and liquidity risks as well as its debt to reserves ratio. As expected, the value of the guarantee increases with the reserves-to-debt ratio, reserves volatility, while decreases with a country's ratings. For instance, the value of IMF liquidity for a Baa-rated country with about 80 percent of its short-term debt by remaining maturity covered by reserves and capital flow volatility of about 10 percent would be about 70 basis points to be assessed at time of qualification. The value of the guarantee is not reported for borrowers in the C categories as these would not qualify for access to IMF contingent liquidity. For countries with large obligations compared to available resources (small dl), the value of the guarantee is not affected by the volatility of its resources in any significant way as the put option is heavily in the money. 3. Conclusion Although not formally enshrined in its articles of agreement, the IMF has often operated as the ultimate provider of international liquidity, most notably in the more recent capital account crises, to deal with an exceptional situation that posed a threat to the stability of the international monetary system. This paper presents a market-based framework for pricing IMF commitment to provide contingent liquidity assistance that accounts for the credit risk and the insurance involved in such operations. It underscores the benefits to the member country of being able to access liquidity when needed. The framework is based on the isomorphic correspondence between IMF liquidity and common stock put options. As a market-based framework, it provides the necessary economic incentives to the prospective borrower, while explicitly assessing the costs for the liquidity provider. Market-signaling issues would need to be dealt with, given that the principle of equality of treatment across the membership is central to the IMF's mandate. However, and while assuming that the IMF should not differentiate risk across its membership, it is worth noting that asset prices may already fully reflect the risk assessment of a specific borrower in orderly functioning markets, which 11 The American put option is used in the simulation as it is the one that would most closely fit a situation in which, after qualification, a member could access Fund liquidity at any time over the lifespan of the instrument. This is indeed the setting under the current proposal for a new liquidity instrument.
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would be the case at the time a member is qualified for access to contingent IMF liquidity. The distinction between lower- and higher-risks would thus reflect public market information. Moreover, the case that the potential differentiation across members would still be consistent with the principle of equality of treatment could be argued on the basis that countries in the same conditions would be assessed the same fee. Finally, the fact that the probability of default is estimated for rating categories, rather than for individual borrowers, may also allay signaling concerns. These signaling concerns need not being overemphasized as, in practice, differences in prices potentially assessed to borrowers according to this approach may not be that significant as the qualification requirement would tend to select a relatively homogenous set of countries. Also, the use of summary indices to assess a member's probability of being illiquid could, in practice, blur differences across the membership. Finally, from a technical viewpoint, the put option is likely to be heavily in the money for the majority of the countries that would have an interest in qualifying for access to contingent IMF liquidity, reflecting large obligations compared to available resources. A country's risk, as assessed by the volatility of its resources, would then have a negligible impact on the value of the put option, evening out the premiums across countries. The numerical examples presented in this paper are only illustrative. They show that the value of the liquidity guarantee provided by accessing IMF liquidity could range from several to almost three hundreds basis points depending on the borrower's creditworthiness, the volatility of capital flows to the borrowing country, and the amount of funds that would be potentially needed to meet the borrower's external obligations. The cost of this liquidity guarantee, which incorporates both credit risk and the instrument's insurance value, would be assessed as a commitment fee upfront. This fee could be refunded in case IMF resources are effectively drawn as per current practices, at which point the charges associated with existing IMF facilities would apply. The level of these commitment fees would need to be evaluated against other design elements of the new liquidity instrument. In practice, there is likely a trade-off between cost and automaticity in accessing liquidity, and different users may aim at a different trade-off. References Black, F., Jones, R., 1987. Simplifying portfolio insurance. Journal of Portfolio Management, Fall 48–51 (Institutional Investor). Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654 (University of Chicago Press). Flood, R., Marion, N., 2002. Holding International Reserves in an Era of High Capital Mobility. IMF working paper No. WP/02/62. Frenkel, J., Jovanovic, B., 1981. Optimal International Reserves: A Stochastic Framework. Economic Journal 91, 507–514. Moody's Investor Service, Sovereign Default and Recovery Rates, 1983–2006, Special Comment June 2007. Ramachandran, M., 2004. The optimal level of international reserves: evidence for India. Economics Letters 83, 365–370 (Elsevier BV, North-Holland). Rossi, M., Zinna, G., 2007. Sovereign Credit Risk: A Rating-Based Perspective. International Monetary Fund, mimeo. Salman, F., Salih, A., 1999. Modeling the volatility in the Central Bank reserves. Research Paper of Central Bank of Turkey. Silva, A.F., da Silva, E., 2004. Optimal international reserves holdings in emerging markets economies: the Brazilian case. www.anpec.org.br/encontro2004/artigos/A04A078.pdf.