We analyze the joint convergence of sequences of discounted stock prices and 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 illustrate the general result by 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.

Keywords : weak convergence, incomplete market, option pricing, minimal martingale measure, stochastic interest rate, trinomial tree.

JEL : D52, E43, G13.
Mathematics Subject Classification (1991) : 60F05, 90A09.