Professor Kai-Sheng Song invites you to attend the

Master's Defense of Aaron Jackson

"A Tree-based Discrete Time Model for Jump Diffusion Option Valuation"

ABSTRACT:

Option pricing models under jump diffusion processes do not, in general, admit closed-form solutions. Even in cases where closed-form formulas are available such as the classic Mertons log-normal jump diffusion model for pricing European options, it is often difficult to explicitly incorporate simple features such as the early exercise feature of American options into the pricing formulas. In such situations, a well-designed discrete time approximation of the jump diffusion process provides a useful and easy to understand alternative. In this talk, we first review the popular binomial tree options pricing method introduced by Sharpe (1978) and subsequently formalized by Cox, Ross, and Rubinstein (1979) for the Black-Scholes model. Then we present an explicit multinomial tree-based discrete time model proposed by Amin (1993) for jump diffusion option valuation. Under some regularity conditions, this discrete time process converges weakly to the original continuous time jump diffusion process and option prices computed from this discrete time model also converge to the option values of their corresponding continuous time model, which justifies such discrete time approximation. Some numerical experiments are also presented to demonstrate the accuracy of this tree-based discrete time algorithm.