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Using Exponential Lévy Models to Study Implied Volatility patterns for Electricity Options

Authors: Pinho C., Madaleno M.

Abstract:

German electricity European options on futures using Lévy processes for the underlying asset are examined. Implied volatility evolution, under each of the considered models, is discussed after calibrating for the Merton jump diffusion (MJD), variance gamma (VG), normal inverse Gaussian (NIG), Carr, Geman, Madan and Yor (CGMY) and the Black and Scholes (B&S) model. Implied volatility is examined for the entire sample period, revealing some curious features about market evolution, where data fitting performances of the five models are compared. It is shown that variance gamma processes provide relatively better results and that implied volatility shows significant differences through time, having increasingly evolved. Volatility changes for changed uncertainty, or else, increasing futures prices and there is evidence for the need to account for seasonality when modelling both electricity spot/futures prices and volatility.

Keywords: Pricing, Calibration, electricity markets, Implied Volatility, Lévy Models, Options on Futures

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085010

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[1] R. Weron, "Heavy-tails and regime-switching in electricity prices," Mathematical Methods of Operations Research Manuscript, vol. 69, no. 3, pp. 457--473, DOI 10.1007/s00186-008-0247-4, 2009.
[2] A. Cartea, and S. Howison, "Option pricing with lévy stable processes generated by lévy stable integrated variance," Quantitative Finance, vol. 9, no. 4, pp. 397-409, 2009.
[3] P. Carr, and L. Wu, "'Stochastic skew in currency options," Journal of Financial Economics, vol. 86, pp. 213--247, 2007.
[4] E. Lindström, "Implications of parameter uncertainty on option prices," Advances in Decision Sciences, vol. 2010, pp.1-15, Article ID 598103, 2010.
[5] M. V. Deryabin, "'Implied volatility surface reconstruction for energy markets: Spot price modelling vs. surface parametrization," Journal of Energy Markets, forthcoming, 2011.
[6] S. Borovkova, and F. J. Permana, "Implied volatility in oil markets," Computational Statistics & Data Analysis, vol. 53, no. 6, pp. 2022-2039, 2009.
[7] F. Black, and M. Scholes, "The pricing of options and corporate liabilities," The Journal of Political Economy, vol. 81, no. 3, pp. 637- 654, 1973.
[8] R. Cont, and J. da Fonseca, "Dynamics of implied volatility surface," Quantitative Finance, vol. 2, pp. 45-60, 2002.
[9] E. Konstantinidi, G. Skiadopoulos, and E. Tzagkaraki, "Can the evolution of implied volatility be forecasted? Evidence from European and US implied volatility indices," Journal of Banking and Finance, vol. 32, no. 11, pp. 2401-2411, 2008.
[10] G. Dotsis, D. Psychoyios, and G. Skiadopoulos, "An empirical comparison of continuous-time models of implied volatility indices," Journal of Banking and Finance, vol. 31, no. 12, pp. 3584-3603, 2007.
[11] D. S. Bates, "'Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, vol. 94, no. 1-2, pp. 181-238, 2000.
[12] G. Bakshi, C. Cao, and Z. Chen, "Empirical performance of alternative option pricing models," The Journal of Finance, vol. LII, no. 5, pp. 2003-2049, 1997.
[13] S.-J. Deng, and W. Jiang, "Lévy process driven mean reverting electricity price model: the marginal distribution analysis," Decision Support Systems, vol. 40, no. 3-4, pp. 483-494, 2005.
[14] F. E. Benth, and J. Saltyte-Benth, "The normal inverse Gaussian distribution and spot price modeling in energy markets," International Journal of Theoretical and Applied Finance, vol. 7, no. 2, pp. 177-192, 2004.
[15] P. Carr, and D. Madan, "Option valuation using the fast fourier transform," The Journal of Computational Finance, vol. 2, no, 4, pp. 61- 73, 1999.
[16] R. Cont, and P. Tankov, "Financial Modelling with Jump Processes," vol. 1. Chapman and Hall/CRC, ISBN 978-1584884132, 2004.
[17] J. W. Cooley, and J. W. Tukey, "An algorithm for the machine calculation of complex fourier series," Mathematics of Computation, vol. 19, no. 90, pp. 297-301, 1965.
[18] R. Merton, "Option pricing when the underlying stock returns are discontinuous", Journal of Financial Economics, vol. 3, pp. 125-144, 1976.
[19] D. B. Madan, and E. Seneta, "'The variance gamma (VG) model for share market returns," Journal of Business, vol. 63, no. 4, pp. 511-524, 1990.
[20] D. B. Madan, P. Carr, and E. C. Chang, "The variance gamma process and option pricing," European Finance Review, vol. 2, pp. 79-105, 1998.
[21] O. E. Barndorff-Nielsen, "Processes of normal inverse Gaussian type," Finance and Stochastics, vol. 2, no. 1, pp. 41-68, 1998.
[22] P. Carr, H. Geman, D. B. Madan, and M. Yor, "The fine structure of asset returns: an empirical investigation," Journal of Business, vol. 75, no. 2, pp. 305-332, 2002.
[23] E. A. Daal, and D. B. Madan, "An empirical examination of the variance-gamma model for foreign currency options," Journal of Business, vol. 78, no. 6, pp. 2121-2152, 2005.
[24] J.-Z. Huang, and L. Wu, "Specification analysis of option pricing models based on time-changed Lévy processes," The Journal of Finance, vol. LIX, no. 3, pp. 1405-1439, 2004.
[25] P. Carr, and L. Wu, "Time-changed Lévy processes and option pricing," Journal of Financial Economics, vol. 71, no. 1, pp. 113-141, 2004.
[26] D. S. Bates, "The crash of '87: Was it expected? The evidence from options markets," The Journal of Finance, vol. 46, no. 3, pp. 1009-1044, 1991.
[27] K. Lam, E. Chang, and M. C. Lee, "An empirical test of the variance gamma option pricing model," Pacific-Basin Finance Journal, vol. 10, no. 3, pp. 267-285, 2002.
[28] D. Edelman, "A Note: Natural Generalization of Black-Scholes in the Presence of Skewness, Using Stable Processes," ABACUS, vol. 31, no. 1, pp. 113-119, 1995.
[29] N. Branger, and C. Schlag, "Why is the Index Smile So Steep?," Review of Finance, vol. 8, no. 1, pp. 109-127, 2004.
[30] J. C. Corrado, and T. W. Miller Jr., "The forecast quality of CBOE implied volatility indexes," Journal of Futures Markets, vol. 25, no. 4, pp. 339-373, 2005.
[31] N. K. Nomikos, and O. A. Soldatos, "Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market," Energy Economics, vol. 32, no. 2, pp. 302-312, 2010.
[32] A. Bouden, "The Behaviour of Implied Volatility Surface: Evidence from Crude Oil Futures Options," Available at SSRN: http://ssrn.com/abstract=930726, Jan. 2007.