Gamma-type operators and the Black–Scholes semigroup

Abstract

We study Gamma-type operators from the analytic and probabilistic viewpoint in the setting of weighted continuous function spaces and estimate the rate of convergence of their iterates towards their limiting semigroup, providing, in this way, a quantitative version of the classical Trotter approximation theorem. The semigroup itself has some interest, since it is generated by the Black-Scholes operator, frequently occurring in the theory of option pricing in mathematical finance.