马尔可夫调制模型下交换期权的定价

在这篇文章中,假定市场经济状态由一个两状态马尔可夫链描述,风险资产满足一个两状态的马尔可夫调制过程。当市场处于高波动状态时,风险资产的价格满足跳扩散过程;当市场处于稳定状态时,风险资产的价格满足几何布朗运动.通过测度变换的技术,得到了交换期权的定价公式。最后,利用蒙特卡洛方法给出了期权价值的数值结果。

Pricing Exchange Options Under a Markov-modulated Model

In this paper,we suppose that the states of market economy are described by a two-state Markov chain,and the risky asset follows a two-state Markov-modulated process.The risky asset price is driven by a Markov-modulated geometric Brownian motion when the market is stable,but the risky asset follows a jump diffusion process if the market is at a high volatility state.We obtain the pricing formula of a exchange option by measure change.Finally,the result of illustration is provided by Monte Carlo simulation technique.