Professor Kai-Sheng Song invites you to attend the Doctoral Dissertation Defense of Ugochukwu Adiele

"Option Pricing Under New Classes of Jump-Diffusion Processes"

ABSTRACT:

Since the seminal work of Merton (1976), incorporating jumps in the celebrated Black-Scholes Brownian motion-based model (1973) has been widely accepted as the standard approach for constructing more realistic models for option prices. Despite its wide use, Merton's jump-diffusion model lacks flexibility in capturing important features such as upward jumps, downward jumps, and the heavy tails of the log returns dynamics. Various extensions such as Kou (2002) have been developed. But none of these generalizations includes Merton's model as a special case. In this talk, we propose two novel classes of exponential jump-diffusion models for pricing options. First, we present the normal convolution with gamma mixture jump-diffusion model. Under this framework, both Merton's jump-diffusion model and Kou's double exponential jump-diffusion model are nested in our model. Our framework unifies several existing methods and yet it remains mathematically tractable. We obtain analytical formulas for pricing European call and put options in terms of easy-to-compute rapidly convergent Kou-type infinite series. Secondly, we present the normal convolution double gamma jump-diffusion model and its analytical solutions for pricing options. This model also generalizes the Merton jump-diffusion model and includes a special case of Kou's double exponential jump-diffusion model. All model parameters in our Monte Carlo simulations are estimated by maximum likelihood under the physical probability measure. We fit our models to some historical data of several stock indices such as S&P 500 and NASDAQ Composite. We also conduct our option pricing model calibration using option data from CBOE. The results demonstrate that our methods outperform both Merton and Kou methods in terms of mean squared prediction errors. Both models are able to reproduce the implied volatility surface observed in the option data.