同质信念与Black-Scholes公式定价偏差——基于期权定价的保险精算方法

Homogeneous Beliefs and Mispricing of Black-Scholes Model Option Pricing Model Based on Actuarial Method

本文分析了包括BS的鞅方法在内的四种期权定价方法.Mogens Bldt和郑红给出的保险精算定价方法是非套利定价,缺少足够的理论基础.另外,存在同质信念的市场上BS定价并非完全无套利,如果对不同股票进行分散化投资,只要基础资产种类足够多,也可套取利益.不同投资者的漂移率取同一常数μ体现了他们的同质信念,与弱有效的现实市场情况相符.进一步分析得出结论,即使存在同质信念,如果μt是一个可料过程而非常数,会使得精算定价难以计算确定期望,从而无效.根据SAS软件的模拟结果,在同质信念下,精算套利定价显著高于BS鞅方法定价.通过恒生股指期权的实证检验,说明同质信念下的漂移率更适合取同一常数而不是可料过程,实证检验发现精算套利理论价格与实际价格差距很小,说明此方法比较有效.

This paper analyzed the four option pricing methods including the martingale method. Mogens Bldt and Hong Zheng gave actuarial pricing methods for options respectively, however, both of the methods are not non-arbitrage lack ade- quate theoretical basis. In addition, BS pricing method is not completely non-arbitrage, for diversified investment at different stock, as long as a sufficient number, may make profit. Moreover, the same drift of stock for different investors embodies homogeneous beliefs, which complies with weak efficient market assumption in real market. Further analysis concludes that, e- ven if homogeneous beliefs exist, the drift of stock could be a previsible process, which results in difficulty to calculate and de- termine the expectations in actuarial pricing and thus invalids the pricing in actuarial method. According to the simulation run by SAS, with homogeneous assumption, actuarial non-arbitrage pricing gives significantly higher price for options than BS. Through empirical test of the Hang Seng index options, the authors believe that, under the assumption of homogeneous be- liefs, the drift should be a constant other than a previsible process and this method is very accurate.