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Pricing Financial Derivatives on Weather Sensitive Assets

Author

Listed:
  • Jerzy Filar

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

  • Boda Kang
  • Malgorzata Korolkiewicz

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

Abstract

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.

Suggested Citation

  • Jerzy Filar & Boda Kang & Malgorzata Korolkiewicz, 2008. "Pricing Financial Derivatives on Weather Sensitive Assets," Research Paper Series 223, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:223
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    File URL: https://www.uts.edu.au/sites/default/files/qfr-archive-02/QFR-rp223.pdf
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    References listed on IDEAS

    as
    1. 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 661-673, June.
    2. Roll, Richard, 1984. "Orange Juice and Weather," American Economic Review, American Economic Association, vol. 74(5), pages 861-880, December.
    3. David H. Cutler & James M. Poterba & Lawrence H. Summers, 1988. "What Moves Stock Prices?," Working papers 487, Massachusetts Institute of Technology (MIT), Department of Economics.
    4. 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.
    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. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    7. 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.
    8. 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.
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    Keywords

    weather-sensitive asset; financial derivatives; diffusion; binomial approximation; numerical methods; time series; actuarial value;

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