The random-time binomial model

In this paper we study a binomial model with random time steps and explain how to calculate values for European and American call and put options. We prove both weak convergence of the discrete processes to the Black–Scholes setup and convergence of the values for European and American put options. Computational experiments exhibit a smooth convergence structure and suggest that we can obtain a quadratic order of convergence via an extrapolation procedure. Approximations to jump-diffusions are straightforward.