马尔可夫调制Merton跳跃扩散即期汇率的货币衍生品定价
Currency Derivatives Pricing for Markov-modulated Merton Jump-diffusion Spot Forex Rate
摘要：
我们得出了类似于Bo等人（2010）的结果，但在外汇汇率动态由一般Merton跳跃扩散过程驱动的情况下。本文的主要结果如下：1）给出了保证贴现外汇汇率的鞅条件是一般Merton跳跃扩散过程的鞅的Esscher变换参数公式;使用这些参数的值，我们继续进行风险神经测量，并提供新的跳跃分布公式，平均跳跃大小，以及关于该测度的Poisson过程强度;给出了欧式看涨外汇期权的定价公式; 2）将所得公式应用于指数过程的情况; 3）对不同参数下的欧式看涨外汇期权价格进行了数值模拟; 4）给出了用于期权价格数值模拟的Matlab函数代码。
英文摘要：
We derived similar to Bo et al. (2010) results but in the case when the dynamics of the FX rate is driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the discounted foreign exchange rate is a martingale for a general Merton jump--diffusion process are derived; using the values of these parameters we proceeded to a risk-neural measure and provide new formulas for the distribution of jumps, the mean jump size, and the Poisson process intensity with respect to the measure; pricing formulas for European call foreign exchange options have been given as well; 2) obtained formulas are applied to the case of the exponential processes; 3) numerical simulations of European call foreign exchange option prices for different parameters are also provided; 4) codes for Matlab functions used in numerical simulations of option prices are given.
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