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Pricing Financial Derivatives on Weather Sensitive Assets

  • Jerzy Filar

    (School of Mathematics and Statistics, University of South Australia)

  • Boda Kang
  • Malgorzata Korolkiewicz

    (School of Mathematics and Statistics, University of South Australia)

We study pricing of derivatives when the underlying asset is sensitive to weather variables such as temperature, rainfall and others. We shall use temperature as a generic example of an important weather variable. In reality, such a variable would only account for a portion of the variability in the price of an asset. However, for the purpose of launching this line of investigations we shall assume that the asset price is a deterministic function of temperature and consider two functional forms: quadratic and exponential. We use the simplest mean-reverting process to model the temperature, the AR(1) time series model and its continuous-time counterpart the Ornstein-Uhlenbeck process. In continuous time, we use the replicating portfolio approach to obtain partial differential equations for a European call option price under both functional forms of the relationship between the weather-sensitive asset price and temperature. For the continuous-time model we also derive a binomial approximation, a finite difference method and a Monte Carlo simulation to numerically solve our option price PDE. In the discrete time model, we derive the distribution of the underlying asset and a formula for the value of a European call option under the physical probability measure.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 223.

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Length: 26 pages
Date of creation: 01 Jun 2008
Date of revision:
Handle: RePEc:uts:rpaper:223
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  1. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
  2. 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 637-54, May-June.
  3. David M. Cutler & James M. Poterba & Lawrence H. Summers, 1988. "What Moves Stock Prices?," NBER Working Papers 2538, National Bureau of Economic Research, Inc.
  4. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
  5. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
  6. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(1), pages 1-20.
  7. Beckers, Stan, 1980. " The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-73, June.
  8. Roll, Richard, 1984. "Orange Juice and Weather," American Economic Review, American Economic Association, vol. 74(5), pages 861-80, December.
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