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Pricing Financial Derivatives on Weather Sensitive Assets

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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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Bibliographic Info

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
Date of creation: 01 Jun 2008
Date of revision:
Handle: RePEc:uts:rpaper:223

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

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  1. 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.
  2. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
  3. 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.
  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. Roll, Richard, 1984. "Orange Juice and Weather," American Economic Review, American Economic Association, vol. 74(5), pages 861-80, December.
  6. 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.
  7. 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.
  8. 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.
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