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Pricing Financial Derivatives on Weather Sensitive Assets

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Author Info
Jerzy Filar (School of Mathematics and Statistics, University of South Australia)
Boda Kang () (School of Finance and Economics, University of Technology, Sydney)
Malgorzata Korolkiewicz (School of Mathematics and Statistics, University of South Australia)

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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.

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

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

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  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 661-73, June. [Downloadable!] (restricted)
  2. Roll, Richard, 1984. "Orange Juice and Weather," American Economic Review, American Economic Association, vol. 74(5), pages 861-80, December. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  5. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(3), pages 393-430. [Downloadable!] (restricted)
  6. David M. Cutler & James M. Poterba & Lawrence H. Summers, 1989. "What Moves Stock Prices?," NBER Working Papers 2538, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  7. Peter Alaton & Boualem Djehiche & David Stillberger, 2002. "On modelling and pricing weather derivatives," Applied Mathematical Finance, Taylor and Francis Journals, vol. 9(1), pages 1-20, March. [Downloadable!] (restricted)
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