Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market
In this paper we examine the importance of mean reversion and spikes in the stochastic behaviour of the underlying asset when pricing options on power. We propose a model that is flexible in its formulation and captures the stylized features of power prices in a parsimonious way. The main feature of the model is that it incorporates two different speeds of mean reversion to capture the differences in price behaviour between normal and spiky periods. We derive semi-closed form solutions for European option prices using transform analysis and then examine the properties of the implied volatilities that the model generates. We find that the presence of jumps generates prominent volatility skews which depend on the sign of the mean jump size. We also show that mean reversion reduces the volatility smile as time to maturity increases. In addition, mean reversion induces volatility skews particularly for ITM options, even in the absence of jumps. Finally, jump size volatility and jump intensity mainly affect the kurtosis and thus the curvature of the smile with the former having a more important role in making the volatility smile more pronounced and thus increasing the kurtosis of the underlying price distribution.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Qiang Dai & Kenneth J. Singleton, 2000.
"Specification Analysis of Affine Term Structure Models,"
Journal of Finance,
American Finance Association, vol. 55(5), pages 1943-1978, October.
- Qiang Dai & Kenneth J. Singleton, 1997. "Specification Analysis of Affine Term Structure Models," NBER Working Papers 6128, National Bureau of Economic Research, Inc.
- Qiang Dai & Kenneth J. Singleton, 1998. "Specification Analysis of Affine Term Structure Models," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-083, New York University, Leonard N. Stern School of Business-.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
- N. K. Nomikos & O. Soldatos, 2008. "Using Affine Jump Diffusion Models for Modelling and Pricing Electricity Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(1), pages 41-71.
- 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.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- 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.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Villaplana, 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.
- Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
- Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
- 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.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
- Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
- repec:dau:papers:123456789/1433 is not listed on IDEAS
- Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
- 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, 06.
- 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.
- Villaplana, Pablo & Peña Sánchez de Rivera, Juan Ignacio & Escribano, Álvaro, 2002. "Modeling electricity prices: international evidence," UC3M Working papers. Economics we022708, Universidad Carlos III de Madrid. Departamento de Economía.
- 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.
- 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.
- repec:dau:papers:123456789/607 is not listed on IDEAS Full references (including those not matched with items on IDEAS)