Stochastic Differential Equations for Derivative Pricing and Energy Risk Management

  • Nigel Da Costa Lewis
Part of the Finance and Capital Markets Series book series (FCMS)


The main objective of this chapter is twofold. First we introduce a number common stochastic processes used in the valuation of derivative contracts and financial simulations. Second, we consider their relevance to energy risk modeling.


Asset Price Stochastic Differential Equation Option Price Energy Price Stochastic Volatility 
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Further Reading

  1. Andersen, L. and Andersen, J. (2000) “Jump-diffusion processes: volatility smile fitting and numerical methods for pricing,” Review of Derivatives Research, 4, 231–62.CrossRefGoogle Scholar
  2. Barz, G. and Johnson, B. (1999) Energy Modelling and the Management of Uncertainty, Risk books, London.Google Scholar
  3. Eraker, B., Johannes, M., and Polson, N. (2003) “The impact of jumps in returns and volatility,” Journal of Finance, 58, 1269–1300.CrossRefGoogle Scholar
  4. Hull, J. and White, A. (1987) “The pricing of options on assets with stochastic volatilities.” Journal of Finance, 42(2), 281–300.CrossRefGoogle Scholar
  5. Hull, J. and White, A. (1988) “An analysis of the bias in option pricing caused by a stochastic volatility.” Advances in Futures and Options Research, 3, 29–61.Google Scholar
  6. Johnson, B. and Graydon, B. (1999) Energy Modelling and the Management of Uncertainty, Risk books, London.Google Scholar
  7. Kat, H. and Heynen, R. (1994) “Volatility prediction: a comparison of the stochastic volatility, GARCH (1,1) and EGARCH (1,1) models,” Journal of Derivatives, 2(2), 50–65.CrossRefGoogle Scholar
  8. Kou, S. (2002) “A jump diffusion model for option pricing,” Management Science, 48(8), 1086–1101.CrossRefGoogle Scholar
  9. Kou, S. and Wang, H. (2004) “Option pricing under a double exponential jump diffusion model,” Management Science, 50(9), 1178–92.CrossRefGoogle Scholar
  10. Merton, R. C. (1976) “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, 3, 125–44.CrossRefGoogle Scholar
  11. Merton, R. C. (1982) Continuous-Time Finance, Paperback edn, Blackwell Publishers Ltd., Cambridge, MA, and Oxford, UK.Google Scholar
  12. Naik, V. (1993) “Option valuation and hedging strategies with jumps in the volatility of asset returns.” The Journal of Finance, 48, 1969–84.CrossRefGoogle Scholar
  13. Ramezani, C. and Zeng, Y. (1998) “Maximum likelihood estimation of asymmetric jump diffusion processes: application to security prices.” Working Paper. Department of Mathematics and Statistics, University of Missouri.Google Scholar
  14. Ramezani, C. (2004) “An empirical assessment of the double exponential jump diffusion process.” Finance Department. Orfalea College of Business. California Polytechnic.Google Scholar
  15. Scott, L. O. (1987) “Option pricing when the variance changes randomly: theory, estimation and an application.” Journal of Financial and Quantitative Analysis, 22, 419–38.CrossRefGoogle Scholar

Copyright information

© Nigel Da Costa Lewis 2005

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  • Nigel Da Costa Lewis

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