Vasicek利率模型下欧式看涨外汇期权定价分析

在Vasicek（瓦西塞克）利率模型下，利用随机微分方程理论中的鞅表示性质，建立了欧式看涨外汇期权本国货币下价格函数所满足的偏微分方程．通过基于鞅理论中测度变换思想的远期变量变换，降低了偏微分方程状态空间的维数，得到了期权的定价公式．此外，定性分析了短期利率、汇率及其波动率变化对期权价格的影响．

Analysis of Pricing European Call Foreign Currency Option Under the Vasicek Interest Rate Model

A pricing problem of European call foreign currency option is studied under the Vastcek model for domestic short interest rate and foreign short interest rate. Using the property of martingale representation on stochastic differential equation theory, a partial different equation for the pricing function in domestic currency of foreign currency option is established. By the method of forward variable translation which is motivated by forward measure in martingale theory, the dimensions of state space of corresponding partial different equation is reduced, and then a closed pricing formula of European call foreign currency option is obtained. In addition, the price evolution of foreign currency option when interest rate and exchange rate and their volatility move, is examined.