Professor Song invites you to attend the PhD Dissertation Defense of Jie Zhou.

WHEN: Thursday, August 5th, at 10:00am

"A New Class of Stochastic Volatility Models for Pricing Options Based on Observables as Volatility Proxies"

ABSTRACT:

One basic assumption of the celebrated Black-Scholes-Merton PDE model for pricing derivatives is that the volatility is a constant. However, the im[1]plied volatility plot based on real data is not constant, but curved exhibiting patterns of volatility skews or smiles. Since the volatility is not observable, various stochastic volatility models have been proposed to overcome the prob[1]lem of non-constant volatility. Among them, the most widely studied models are those stochastic volatility models proposed by Hull and White (1987), Stein and Stein (1991), and Heston (1993). Although these methods are fairly successful in modeling volatilities, they still rely on the implied volatil[1]ity approach for model implementation. To avoid such circular reasoning, we propose a new class of stochastic volatility models based on directly observ[1]able volatility proxies and derive the corresponding option pricing formulas. In addition, we propose a new GARCH (1,1) model, which is different from that of Heston and Nandi (2000), and show that this discrete-time stochastic volatility process converges weakly to Heston's continuous-time stochastic volatility model. Some Monte Carlo simulations and real data analysis are also conducted to demonstrate the performance of our methods.