KoBol分数阶期权定价模型的数值方法

Numerical Method for KoBol Fractional Option Pricing Model

摘要:

自Black-Scholes期权定价模型提出以来， 大量的期权定价模型被陆续提出并加以研究，成为国内外金融工程和金融数学的研究热点。由于列维过程能够很好地描述资产运动的动力学特征， 近年来基于列维过程的期权定价模型吸引了广泛关注， 如FMLS（finite moment log stable）、CGMY和KoBol模型。这些模型最终归结为数值求解一类分数阶偏微分方程。为此提出了求解这类分数阶偏微分方程的数值离散格式， 理论分析给出了数值格式稳定的充分条件。数值实验验证数值格式和算法的可行性和有效性。基于上证50与沪深300的股指期权实际交易数据， 利用KoBol分数阶模型进行定价并反演计算波动率曲线， 进一步验证了KoBol模型在真实市场中的有效性。

Abstract:

Since the Black-Scholes model was proposed， many option pricing models have been proposed， which has become a hotspot in financial engineering. For the past few years， option pricing models based on Lévy process such as FMLS， CGMY and KoBol have drawn great attention because of their capability to represent the dynamic characteristics of underlying asset. Solving these models would eventually come down to solving a class of fractional partial differential equations. In this paper， a numerical scheme is proposed for the class of FPDE and the stable condition of the scheme is given. The numerical experiments prove the feasibility and effectiveness of the proposed numerical scheme. Based on the practical data of SSE 50ETF and CSI 300ETF index option， the option price and volatility curve are calculated to verify the effectiveness of KoBol model in real market.