非仿射随机波动率的欧式回望期权定价

摘要

经典的Black-Scholes模型将金融衍生产品的价格表示为标的股票价格和常数波动率的函数,与实际市场并不相符.为了克服隐含波动率的"微笑"效应,将股价波动率作为另一个随机过程即随机波动率模型是对经典模型的一个重要改进.假定标的股票价格及其波动率服从非仿射随机波动率模型,研究具有强路径依赖特征的回望期权的定价问题.首先应用蒙特卡罗模拟法分别模拟出波动率过程和股票价格过程的路径,接着给出了期权定价的具体算法,并采用对偶方差减小技术求出欧式回望期权价格的数值解.最后,通过数值实例分析了期权的价格.%The classical Black-Scholes model takes the price of financial derivatives as a function of the stock price and the constant volatility,which is not consistent with the actual market.And in order to overcome the im-plied volatility "smile" effect,there is an important improvement on the classical model,which takes the stock price volatility as a stochastic process.In this paper,we study the non-affine stochastic volatility model and focus on the pricing of lookback option which is path-dependent.We first simulate the processes of the volatility rate and the price of the stock by the dual variable Monte Carlo method. Secondly,we develop an effective algorithm for pricing lookback option and find the approximate price of the lookback option. Finally,we illustrate our results with one example about numerical calculation for pricing the lookback option.