混合高斯Heston资产定价模型及统计模拟分析

Mixed Gaussian Heston Asset Pricing Model and Statistics Simulation Analysis

摘要: 经典Heston模型没有考虑资产的长相依性,金融实践证明其不能很好的刻画资产的真实情况. 本文建立了混合高斯~Heston~资产定价模型, 利用股票数据进行实证分析. 首先, 得到了混合高斯~Heston~模型满足的随机偏微分方程, 并讨论了解的存在性和唯一性以及~p~阶矩性质. 其次, 对模型中未知参数进行估计和敏感性分析, 通过~3~只股票的实际数据对~Heston~模型、混合高斯~Heston~模型满足的价格路径与真实路径做了对比. 研究表明: 混合高斯~Heston~模型比经典的~Heston~模型更能够刻画资产标的价格.

Abstract: The classical Heston model does not consider no long-term dependence of asset, and the financial empirical analysis proves that it can not describe the real situation of assets well. In this article, the mixed Gaussian Heston model is established and stocks data are analyzed. Firstly, the existence and uniqueness of the solution and the properties of the p-order moment of the solution are discussed, respectively. Secondly, the unknown parameters in the model are estimated and the sensitivity analysis are carried out. The actual data of three stocks are used to compare the price path satisfied by Heston model and mixed Gaussian Heston model with the real path. It shows that the mixed Gaussian Heston model can describe the asset price better than the Heston model.vvv