报告题目：Expansion aroundBlack-Scholes-Merton: A New Approximation for Option Pricing under StochasticVolatility with Jumps

报 告 人：李辰旭 副教授，北京大学光华管理学院

时    间：2017.05.19(周五) 9:30-10:30

地    点：金融工程研究中心学术报告厅览秀楼105

摘    要： We develop a new approach to approximate option prices under stochasticvolatility with jump models, which are lacking of analytical solutions ingeneral. Our approach can be regarded as an intuitive path expansion withrespect to the stochastic volatility. Accordingly, the approximation naturallygeneralizes and corrects the celebrated formula of Merton (1976) for pricingoptions under jump-diffusions with constant volatility. Such a novel idearesembles the Taylor expansion in classical calculus but is deeply rooted in Malliavincalculus. Our expansion is convenient to implement up to an arbitrary order inprinciple. Following the idea of Ait-Sahalia and Kimmel (2007) and applying ourprice approximation, we develop and implement a method of maximum likelihoodestimation for the models by setting option prices as proxies for the latentvolatility factors. Using the data of S&P500 and its option prices, weestimate an exponential Ornstein-Uhlenbeck type stochastic volatility with jumpmodel, which allows double-sided jump in volatility. Our empirical findingsreveal that the model outperforms many nested models and, in particular,support the stylized fact of double-sided jumps in volatility.