有限状态Q过程积分分布及在衍生证券定价中的应用

Distribution of Q Process Integral and its Application in the Black and Scholes Equation

摘要: 原始Black-Scholes公式中扩散系数σ_t被视为常数,无法表现金融数据收益率厚尾和波动聚类的统计特征,本文尝试用有限状态Q过程描述扩散系数σ_t,理论和实证的结果都优于原始Black-Scholes公式。解决问题的核心是有限状态Q过程积分分布的近似计算和相应的统计问题。

Abstract: Options are financial instruments designed to protect investors from the stock market randomness. In 1973, Black, Scholes and Merton proposed a very popular option pricing method using stochastic differential equations within the Itô interpretation. We give a analysis and numerical simulations for a Black and Scholes equation with Q process volatility.