基于时间变换和分数型过程下的期权定价及模拟分析

Option Pricing Based on Time-Transform and Fractional Process and Simulation Analysis

摘要: 由布朗运动驱动的期权定价模型是最为经典的模型,但该模型不能准确地描述资产价格的长相依性和短时间的不变性.本文提出了时间变换下的次分数布朗运动支付红利期权定价模型. 首先,建立了次分数布朗运动扩散~B-S~模型, 获得了带红利的欧式期权定价公式. 其次,利用金融实际数据进行统计模拟, 研究表明新模型能够反映金融资产真实值.

Abstract: Model of option pricing driven by Brownian motion is the most classical model. However, it can not describe long-term property and invariance in a short period of time of asset price. In this article, option pricing model driven by sub-fractional Brownian motion is studied under time-transform with dividend-paying. Firstly, the model of diffusion B-S model of sub-fractional Brownian motion is build, and get option pricing formula with dividends. Secondly, statistical simulation is used by real data in finance and show that new model can reflect real financial assets.