标的资产的对数收益非正态时的亚式期权的定价

Asian Option Valuation for Non-Gaussian Log Return of Underlying Security

在标的资产的对数收益非正态的情况下,本文通过时间序列的动态结构推导出股票对数收益的Edgeworth展开,由此推导几何平均亚式期权值,并看出对数收益过程的非高斯性及相依性对期权定价的影响。

Black and Scholes provided the foundation of modern option pricing thoery.However,the B-S thoery entails some inconsistencies.In particular,the B-S model assumes that stock prices follow a geometric Brownian motion with a comstant volatility under an equivalent martingale measure.In fact,a lot of finacial empirical studies show that the price process follows non-Gaussian and isn＇t geometric.In order to avoid this drawback,some people approximate the risk-netural density by a statistical series expansion and approximate the density of the state price by an Edgeworth series expansion involving the log-normal density. Under the non-Gaussianity of the stock log return, this paper derives the Edgeworth expansion for the stock log return via extracting dynamics structure of time series, then using the result, we can derive geometric mean Asian option pricing and we investigate the influencse of the non-Gaussianity and the dependency of log return processes for option pricing.