【摘要】 我们用一个受约束的跳扩散模型描述汇率行为,利用傅里叶逆变换给出欧式外汇看涨期权价格的解析解,并用Monte Carlo模拟来展示有约束模型与传统没有约束模型在期权定价上的差异.由于中国实行有管理的浮动汇率制度,我们的研究可以应用于中国外汇市场上人民币外汇期权的定价分析.更多还原

【Abstract】 The previous literature about option pricing usually assumes that the underlying asset follows some kind diffusion process models. Black—Scholes( 1973) assumes the underlying asset follows the Geometric Brownian motion. As underlying asset price may be discontinued,Merton( 1976) suggested a jump-diffusion process model be used to describe it. Heston( 1993) observe that the volatility of underlying asset price may change. Thus,he suggested that the underlying asset follows a stochastic volatility model. Given the underlying asset price behavior model,Black-Scholes( 1973),Merton( 1976) and Heston( 1993) propose their own option pricing formulas.However,regulating asset price is common in the real world. For example,the range for RMB exchange rate is controlled with certain limit. In this situation the underlying asset price behavior models are not suitable for describing RMB exchange rate.In this paper,we use a restricted jump—diffusion model to describe the dynamics of managed foreign exchange rate. At first we use Merton’s( 1976) model to describe exchange rate dynamics. If the daily change exceeds a given interval by exchange rate regulations,we use boundary value as the exchange rate. Otherwise,Merton’s( 1976) model is used. We propose three functions to analyze the exchange rate process based on the restricted jump—diffusion model. The restricted jump—diffusion model can properly describe the dynamics of managed exchange rate.We derive the analytical price formula for European call option of foreign currency under our restricted jump-diffusion model using Fourier inverse. Using call-put parity,put option price formula can be easily obtained. Our proposed formula is similar to BlackScholes-Merton’s.We ran the Monte Carlo simulation and the result shows that our restricted jump-diffusion model is significantly different from Merton’s( 1976) jump-diffusion model. Numerical solutions of European call option for our restricted jump-diffusion model and Merton’s( 1976) jump-diffusion model are derived by using the same parameters. The relationship between price regulation and option price is discussed with respect to the difference between our model and Merton’s.Our methodology can be used to compute European option price for the underlying asset following restricted jump—diffusion model,regardless whether the underlying asset is stock or future. In addition,the proposed model can be used to analyze pricing option with stochastic interest rate and stochastic volatility.更多还原