Explicit formula for conditional expectations of product of polynomial and exponential function of affine transform of extended cox-ingersoll-ross process

Abstract

In this thesis an explicit formula for conditional expectations of the product of polynomial and exponential function of an affine transform is derived under the extended function of an transform is derived under the extended Cox-Ingersoll-Ross (ECIR) process. By applying the Feynman-Kac theorem, the explicit formula is revealed from the solution of the corresponding partial differential equation. To support the validity of the obtained results, we, herein, conduct Monte Carlo simulations to investigate the accuracy of the explicit formula.