基于改进Heston模型的欧式期权定价
European Option Pricing Based on Improved Heston Model
DOI: 10.12677/AAM.2020.91015, PDF,    科研立项经费支持
作者: 江 倩：广西大学数学与信息科学学院，广西 南宁
关键词: 随机波动率；PDE方程；欧式期权；定价；Random Volatility； the PDE Equation； European Option； Pricing
摘要: Heston模型是一种被广泛应用于资产管理的随机波动率(SV)模型。本文设置动态的均值回复幂函数代替Heston模型采用均值回复平方根描述波动率过程，提出一种改进的Heston模型，并根据实际确定幂函数具体形式。利用∆-对冲原理构造无风险资产组合，得到该模型下期权价格满足的PDE，以及利用反演定理求期权价格的封闭形式解。实证分析表明，改进的Heston模型能有效提高模型定价的准确性。
Abstract: Heston model is a stochastic volatility (SV) model widely used in asset management. In this paper, a dynamic mean reversion power function is set to replace the Heston model which used the mean reversion square root to describe the volatility process. An improved Heston model is proposed and the specific form of power function is determined according to the actual situation. Using the ∆-hedging principle, we construct a risk-free asset portfolio, get the PDE of option price satisfying the model, and use the inversion theorem to find the closed form solution of option price. Empirical analysis shows that the improved Heston model can effectively improve the accuracy of pricing.
文章引用：江倩. 基于改进Heston模型的欧式期权定价[J]. 应用数学进展, 2020, 9(1): 120-132. https://doi.org/10.12677/AAM.2020.91015

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