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Pricing power derivatives: a two-factor jump-diffusion approach

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  • Villaplana Conde, Pablo

Abstract

We propose a two-factor jump-diffusion model with seasonality for the valuation of electricity future contracts. The model we propose is an extension of Schwartz and Smith (Management Science, 2000) and Lucia and Schwartz (Review of Derivatives Research, 2002), long-term / short-term model. One of the main contributions of the paper is the inclusion of a jump component, with a non-constant intensity process (probability of occurrence of jumps), in the short-term factor. We model the stochastic behaviour of the underlying (unobservable) state variables by Affine Diffusions (AD) and Affine Jump Diffusions (AJD). We obtain closed form formulas for the price of futures contracts using the results by Duffie, Pan and Singleton (Econometrica, 2000). We provide empirical evidence on the observed seasonality in risk premium, that has been documented in the PJM market. This paper also complements the results provided by the equilibrium model of Bessembinder and Lemmon (Journal of Finance, 2002), and provides an easy methodology to extract risk-neutral parameters from forward data.

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  • Villaplana Conde, Pablo, 2003. "Pricing power derivatives: a two-factor jump-diffusion approach," DEE - Working Papers. Business Economics. WB wb031805, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
  • Handle: RePEc:cte:wbrepe:wb031805
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    References listed on IDEAS

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    1. Narasimhan Jegadeesh & George Pennacchi, 1996. "The behavior of interest rates implied by the term structure of Eurodollar future," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 426-451.
    2. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    3. Hirshleifer, David, 1990. "Hedging Pressure and Futures Price Movements in a General Equilibrium Model," Econometrica, Econometric Society, vol. 58(2), pages 411-428, March.
    4. Longstaff, Francis A & Wang, Ashley, 2002. "ELECTRICITY FORWARD PRICES: A High-Frequency Empirical Analysis," University of California at Los Angeles, Anderson Graduate School of Management qt3mw4q41x, Anderson Graduate School of Management, UCLA.
    5. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    6. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
    7. Hendrik Bessembinder & Michael L. Lemmon, 2002. "Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets," Journal of Finance, American Finance Association, vol. 57(3), pages 1347-1382, June.
    8. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
    9. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    10. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1998. "The Central Tendency: A Second Factor In Bond Yields," The Review of Economics and Statistics, MIT Press, vol. 80(1), pages 62-72, February.
    11. Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    12. George Chacko, 2002. "Pricing Interest Rate Derivatives: A General Approach," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 195-241, March.
    13. Longstaff, Francis & Wang, Ashley, 2002. "Electricity Forward Prices: A High-Frequency Empirical Analysis," University of California at Los Angeles, Anderson Graduate School of Management qt7mh2m2bt, Anderson Graduate School of Management, UCLA.
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    Cited by:

    1. Nomikos, Nikos K. & Soldatos, Orestes A., 2010. "Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market," Energy Economics, Elsevier, vol. 32(2), pages 302-312, March.
    2. Weron, Rafal, 2008. "Market price of risk implied by Asian-style electricity options and futures," Energy Economics, Elsevier, vol. 30(3), pages 1098-1115, May.
    3. Kanamura, Takashi & O[combining macron]hashi, Kazuhiko, 2008. "On transition probabilities of regime switching in electricity prices," Energy Economics, Elsevier, vol. 30(3), pages 1158-1172, May.
    4. Nomikos, Nikos K. & Soldatos, Orestes A., 2010. "Modelling short and long-term risks in power markets: Empirical evidence from Nord Pool," Energy Policy, Elsevier, vol. 38(10), pages 5671-5683, October.
    5. Mari, Carlo, 2006. "Regime-switching characterization of electricity prices dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 552-564.
    6. Guo, Zi-Yi, 2017. "Models with Short-Term Variations and Long-Term Dynamics in Risk Management of Commodity Derivatives," EconStor Preprints 167619, ZBW - German National Library of Economics.
    7. Shao, Chengwu & Bhar, Ramaprasad & Colwell, David B., 2015. "A multi-factor model with time-varying and seasonal risk premiums for the natural gas market," Energy Economics, Elsevier, vol. 50(C), pages 207-214.
    8. Islyaev, Suren & Date, Paresh, 2015. "Electricity futures price models: Calibration and forecasting," European Journal of Operational Research, Elsevier, vol. 247(1), pages 144-154.
    9. Jan Seifert & Marliese Uhrig-Homburg, 2007. "Modelling jumps in electricity prices: theory and empirical evidence," Review of Derivatives Research, Springer, vol. 10(1), pages 59-85, January.

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