基于马尔科夫状态转移模型的天气衍生品定价

杨  刚1; 杨徐进2

基于马尔科夫状态转移模型的天气衍生品定价

引用本文：杨刚1 ,杨徐进2.基于马尔科夫状态转移模型的天气衍生品定价[J].经济数学,2020,(2):16-23

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作者	单位
杨刚1 ,杨徐进2	（1.湖南工商大学数学与统计学院,湖南长沙 410205；2.湖南工商大学财政金融学院，湖南长沙 410205）

中文摘要:引入马尔科夫状态转移(MRS)模型拟合长沙市每日平均气温变化，利用最大期望算法估计马尔科夫状态转移模型参数，通过误差分析得到了最佳MRS模型.基于最佳的MRS模型，采用无套利定价原理定价气温衍生品，并利用蒙特卡罗方法得到了取暖指数（HDD）欧式看涨期权的数值解.实证结果表明，五状态的MRS模型对长沙市每日平均气温变化的拟合效果明显优于其他的MRS模型，它使得气温衍生品定价结果相比以前的方法更为精确.

中文关键词:数量经济学最优气温模型 EM算法无套利定价原理天气衍生品 MRS模型

Weather Derivatives Pricing Based on Markov Regime-switching Model

Abstract:The Markov regime-switching model is introduced to fit the variation of Changsha daily average temperature. The parameters of Markov regime-switching (MRS) models are estimated by Expectation-Maximization algorithm. The optimal MRS model is derived by error analysis. On the basis of the optimal MRS model, no-arbitrage pricing principle is applied to pricing the temperature derivatives. Numerical solution to the HDD European call option is determined by Monte Carlo method. As the empirical result is shown, the fitting effect of five-state-MRS model for the variation of Changsha daily average temperature is superior to other MRS models. Hence, the pricing result of temperature derivatives is more accurate than ever.

keywords:quantitative economics optimal temperature model EM algorithm no-arbitrage pricing principle weather derivatives MRS model

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