Abstract

This paper derives a closed-form expansion for the conditional expectation of a continuous-time stochastic process, given by V<inf>t,T</inf>:=e^{−∫<inf>t</inf>^Tg(v<inf>s</inf>)ds}f(v<inf>T</inf>) for 0≤t≤T, where v<inf>t</inf> evolves according to the extended Cox-Ingersoll-Ross process, for any C^∞ functions f and g. We apply the Feynman-Kac theorem to state a Cauchy problem associated with V<inf>t,T</inf> and solve the problem by using the reduction method. Furthermore, we extend our method to any piecewise C^∞ function f; demonstrating our method can be applied to price options in financial derivative markets. In numerical study, we employ Monte Carlo simulations to demonstrate the performance of the current method.