×

A jump diffusion model for spot electricity prices and market price of risk. (English) Zbl 1402.91936

Summary: We construct a jump-diffusion model with seasonality, mean-reversion, time-dependent jump intensity and heteroskedastic disturbance for electricity spot prices, while keeping the analytical tractability of futures prices. We find that the jump component plays a considerably larger role than the diffusion component in the variance of spot prices. Moreover, the jump intensity is much higher during summer and winter. We also explore the seasonal market price of risk (MPR) with different maturities, from one month to five months. Our results show that the diffusion risk and the jump risk are priced quite differently.

MSC:

91G80 Financial applications of other theories
91B24 Microeconomic theory (price theory and economic markets)
93E11 Filtering in stochastic control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bierbrauer, M.; Menn, C.; Rachev, S. T.; Trück, S., Spot and derivative pricing in the EEX power market, Journal of Banking and Finance, 31, 3462-3485, (2007)
[2] Mugele, C.; Rachev, S. T.; Trück, S., Stable modeling of different European power markets, Investment Management and Financial Innovations, 2, 3, 65-85, (2005)
[3] Deng, S.; Oren, S., Electricity derivatives and risk management, Energy, 31, 940-953, (2006)
[4] Pan, J., The jump-risk premia implicit in options: evidence from an integrated time-series study, Journal of Financial Economics, 63, 1, 3-50, (2002)
[5] P. Villaplana, Pricing power derivatives: a two-factor jump-diffusion approach, Working Paper, 2003.
[6] Escribano, Á; Peña, J. I.; Villaplana, P., Modelling electricity prices: international evidence, Oxford Bulletin of Economics and Statistics, 73, 5, 622-650, (2011)
[7] Eydeland, A.; Geman, H., Pricing power derivatives, Risk, 71-73, (1998)
[8] Schwartz, E.; Smith, J. E., Short-term variations and long-term dynamics in commodity prices, Management Science, 46, 7, 893-911, (2000)
[9] Duffie, D.; Pan, J.; Singleton, K., Transform analysis and asset pricing for affine jump-diffusions, Econometrica, 68, 6, 1343-1376, (2000) · Zbl 1055.91524
[10] Lucia, J. J.; Schwartz, E., Electricity prices and power derivatives: evidence from nordic power exchange, Review of Derivatives Research, 5, 1, 5-50, (2001) · Zbl 1064.91508
[11] Bhanot, K., Behavior of power prices: implications for the valuation and hedging of financial contracts, Journal of Risk, 2, 43-62, (2000)
[12] Weron, R.; Bierbrauer, M.; Trück, S., Modeling electricity prices: jump diffusion and regime switching, Physica A: Statistical and Theoretical Physics, 336, 1-2, 39-48, (2004)
[13] Longstaff, F. A.; Wang, A. W., Electricity forward prices: a high-frequency empirical analysis, Journal of Finance, 59, 4, 1877-1900, (2004)
[14] Viehmann, J., Risk premiums in the German day-ahead electricity market, Energy Policy, 39, 1, 386-394, (2011)
[15] Novikov, A. A., On an identity for stochastic integrals, Theory of Probability and its Applications, 17, 4, 717-720, (1973) · Zbl 0284.60054
[16] Girsanov, I. V., On transforming a certain class of stochastic processes by absolutely continuous substitution of measures, Theory of Probability and its Applications, V, 3, 285-305, (1960) · Zbl 0100.34004
[17] Øksendal, B.; Sulem, A., Applied stochastic control of jump diffusions, (2004), Springer
[18] Björk, T., Bond market structure in the presence of marked point processes, Mathematical Finance, 7, 2, 211-223, (1997) · Zbl 0884.90014
[19] Schönbucher, P. J., (Credit Derivatives Pricing Models: Models, Pricing and Implementation, The Wiley Finance Series, (2003), John Wiley & Sons)
[20] Kim, C.-J.; Nelson, C. R., State-space models with regime switching: classical and Gibbs sampling approaches with applications, (2000), The MIT Press
[21] Chang, K.-H.; Kim, M.-J., Jumps and time-varying correlations in daily foreign exchange rates, Journal of International Money and Finance, 20, 611-637, (2001)
[22] Hamilton, J. D., Time series analysis, (1994), Princeton University Press · Zbl 0831.62061
[23] Bhar, R., Stochastic filtering with applications in finance, (2010), World Scientific Publishing Company · Zbl 1255.91003
[24] Shawky, H. A.; Marathe, A.; Barrett, C. L., A first look at the empirical relation between spot and futures electricity prices in the united states, Journal of Futures Markets, 23, 10, 931-955, (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.