A Closed-Form Approximation for Pricing Temperature-Based Weather Derivatives
A Closed-Form Approximation for Pricing Temperature-Based Weather Derivatives作者机构：School of Economics and Finance Queensland University of Technology Brisbane Australia
出 版 物：《Applied Mathematics》 (应用数学（英文）)
年 卷 期：2013年第4卷第9期
页 面：1347-1360页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Weather Derivatives Temperature Models Cooling-Degree Days Distributions for Correlated Variables
摘 要：This paper develops analytical distributions of temperature indices on which temperature derivatives are written. If the deviations of daily temperatures from their expected values are modelled as an Ornstein-Uhlenbeck process with timevarying variance, then the distributions of the temperature index on which the derivative is written is the sum of truncated, correlated Gaussian deviates. The key result of this paper is to provide an analytical approximation to the distribution of this sum, thus allowing the accurate computation of payoffs without the need for any simulation. A data set comprising average daily temperature spanning over a hundred years for four Australian cities is used to demonstrate the efficacy of this approach for estimating the payoffs to temperature derivatives. It is demonstrated that expected payoffs computed directly from historical records are a particularly poor approach to the problem when there are trends in underlying average daily temperature. It is shown that the proposed analytical approach is superior to historical pricing.
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