基于价格随机波动率的衍生产品期权定价

Pricing of Derivatives Option with Stochastic Prices Volatility

为了研究随机波动率对期权定价的影响,应用解偏微分方程与特征函数方法,建立了基于价格随机波动率的欧式买权定价模型.该模型允许基础资产价格的波动率与其收益率相关,并证得欧式买权的价格与基础资产价格过程的漂移项无关.在允许随机利率情况下,应用该模型进一步给出了债券期权和外汇期权的定价公式,结果表明它对期权定价有重要作用.

In order to analyze the effects of stochastic on the option prices, a new technique based on partial differential equation and characteristic functions was used to establish the closed-form pricing formula of European option model. The model allows arbitrary correlation between volatility and spot-asset returns, and that the price of European option is independent of the drift of the asset price is proved. Furthermore, in the case that the stochastic interest rates are allowed, the pricing formulas of bond options and currency options can be further given by the model. The conclusion shows that stochastic volatility plays an important role in option pricing.