收益率服从q-高斯分布的二叉树期权定价模型及实证分析

Binary Tree Option Pricing Model with q-Gaussian Distribution of Return and Empirical Analysis

以股票价格收益率服从q-高斯分布为基础,使用二叉树定价方法,得到收益率符合q-高斯分布的新型二叉树期权定价模型及数值解法;以部分2023年中证1000和上证50的股指期权价格数据为样本,利用MATLAB进行参数估计、模拟计算股指期权看涨期权价格,并进行图像拟合;最后,对一般二叉树模型、新型二叉树模型所求价格与实际期权价格进行比较,得出收益率服从q-高斯分布的新型二叉树期权定价模型更优的结论,为收益率具有尖峰厚尾特征的相关股指期权定价问题提供了一定的方法和依据.

Firstly,based on the q-Gaussian distribution of stock price returns,a new binary tree option pricing model and numerical solution with q-Gaussian distribution of returns are obtained by using the binary tree pricing method.Secondly,using partial stock index option price data of CSI 1000 and SSE 50 in 2023 as samples,MATLAB is used for parameter estimation,simulation calculation of stock index option call option prices,and image fitting.Finally,by comparing the prices obtained by the general binary tree model and the new binary tree model with the actual option prices,it is concluded that the new binary tree option pricing model with a q-Gaussian distribution of returns is better.This study provides a certain method and basis for the pricing problem of stock index options with sharp peaks and thick tails of returns.