中国股市权证定价的带均值回归跳跃扩散模型

Mean-reverting jump-diffusion model of China stock warrants

针对中国股价运动规律,提出一个带均值回归项的跳跃扩散模型,并以上证指数数据为例,给出模型的参数估计方法.结果表明该定价模型在单边市的情形下,能够比传统B-S公式更好的体现中国股市动态资产价格的运动过程.此外,还给出了基于带均值回归项的跳跃扩散模型的各种类型权证(美式、欧式和百慕大式)的模拟定价方法,并给出此模拟定价方法的实证结果.结果表明,该模型的对中国股市的拟合程度明显好于经典Black-Scholes期权定价公式.

This paper presents a mean-reverting jump-diffusion model, with respect to recently China stock market movements. We also provide the statistical method of calibrating parameters, and give a calculate example of Shanghai stock index. The result shows that this model can take bulls, bears and shock into account, giving a very good fit of China stock dynamic assets movements. In addition, this paper also discusses pricing warrants （including European-Style, American-Style, and Bermuda-Style） under the proposed mean-regression jump-diffusion model.