Consistent Pricing of S&P500 and VIX Options
日期: 2022-01-11

Consistent Pricing of S&P500 and VIX Options


练光华博士,瑞士联邦银行(UBS)亚太区权益类量化交易部量化总监,南方科技大学金融系业界导师。此前获得加州伯克利大学金融工程硕士(MFE)学位,澳大利亚Wollongong大学博士学位,和澳大利亚Adelaide大学博士后。他担任过南澳大利亚大学的讲师(北美助理教授)以及高级讲师终身职位,并在摩根斯坦利银行期权交易部担任量化策略分析师。他的主要研究方向为衍生品定价和风险管理、波动率模型、量化交易、时间序列分析等。科研成果发表于Mathematical Finance, Journal of Banking and Finance, Journal of Economic Dynamics and Control, Quantitative Finance, Journal of Futures Markets等国际期刊。


This paper introduces a three-factor stochastic volatility model to consistently price options written on the S&P500 stock index and volatility index (VIX). The non-affine structure of the model leads to analytical intractability so closed-form pricing formulae may not exist either for S&P500 options, or for VIX options. This study firstly proposes two analytical asymptotic formulae to efficiently price S&P500 options and VIX options, respectively, based on the three-factor stochastic volatility model. By applying singular perturbation techniques, our formulae are obtained by solving a set of partial differential equation systems. We then rigorously justify the convergence of the asymptotic formulae. In addition, we present some numerical examples to demonstrate that our asymptotic formulae can achieve high efficiency and accuracy for a large class of options with relative short tenor. We then present empirical experiments with options data in 2021 showing that our model can simultaneously fit prices of S&P500 options and VIX options. We also show that our model reduces the errors of the SPX and VIX options compared to the single-scale model of Heston.