Applied Mathematics Seminar



SPEAKERProfessor Tai-Ho Wang]Department of Mathematics, Baruch College, CUNY^

TITLEBridge Representation and Small Time Approximation of Transition Density

ABSTRACT In this talk we present a bridge representation for the transition density of stochastic process driven by either standard Brownian motions or mixed Brownian and fractional Brownian motions. A small time approximation of the transition density is readily obtained by approximate the bridge representation by a single deterministic path, which in the classical case recovers the heat kernel expansion for diffusion processes. Applications of such small time approximations include small time asymptotics for prices and implied volatilities of European or Asian equity options as well as options on realized variance.