Option Pricing when the Regime-Switching Risk is Priced  

作　　者：Tak Kuen Siu Hailiang Yang 

机构地区：[1]Department of Mathematics and Statistics, Curtin University of Technology, Perth, W.A. 6845, Australia [2]Department of Statistics and Actuarial Science, the University of Hong Kong, Pokfulam Road, Hong Kong

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第3期369-388,共20页应用数学学报（英文版）

基　　金：the Research Grants Councilof the Hong Kong Special Administrative Region,China(Project No.HKU 754008H)

摘　　要：We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two- stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.

关 键 词：Option valuation regime-switching risk two-stage pricing procedure Esscher transform martingale restriction min-max entropy problem 

分 类 号：O211.6[理学—概率论与数理统计]