Speaker’s Name: Jaehyuk Choi (Assistant Prof./Peking University HSBC Business School)
This study concerns normal stochastic volatility (NSV) model in which the price follows an arithmetic Brownian motion. The NSV model provides a better option pricing model for some asset classes, such as interest rate, compared to its counterpart based on Black-Scholes-Merton model.
In a broader context, the distribution under NSV model gives a leptokurtic distribution generalizing normal distribution. We consider a class of NSV model whose volatility process is given as a geometric Brownian motion, which includes the zero beta case of the Stochastic-Alpha-Beta-Rho (SABR) model. Based on the two generalized Bugerol’s identities proved by Alili and Gruet (1997), the distribution is expressed as a transformation of normal random variables, which
enables us to efficiently draw the random numbers and price vanilla options. We provide three methods for parameter estimation; moments matching, calibration to implied volatility smile and maximum likelihood estimation. We also show that a special case of our model results in the unbounded Johnson distribution, which is a popular choice for leptokurtic distribution. Therefore this study not only provide the underlying dynamics for Johnson distributions but also generalizes the distribution family.