Pricing Financial Derivatives on Weather Sensitive Assets

Jerzy Filar, Boda Kang and Malgorzata Korolkiewicz
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Jerzy Filar: School of Mathematics and Statistics, University of South Australia
Malgorzata Korolkiewicz: School of Mathematics and Statistics, University of South Australia

No 223, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: weather-sensitive asset; financial derivatives; diffusion; binomial approximation; numerical methods; time series; actuarial value (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fmk
Date: 2008-06-01
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