Convergence of Discrete Time Options Pricing Models under Stochastic Rates

We analyze the joint convergence of sequences of discounted stock prices and the Radon-Nicodym derivatives of the minimal martingale measure when interest rates are stochastic. Therefrom we deduce the convergence of option values in either complete or incomplete markets. We particularize the general reuslt to two main examples: a discrete time i.i.d. approximation of a Merton type pricing model for options on stocks and the trinomial tree of Hull and White for interest rate derivatives.