Convergence from Discrete- to Continuous-Time Contingent Claims Prices

This article generalizes the Cox, Ross, and Rubinstein (1979) binomial option-pricing model, and establishes a convergence from discrete-time multivariate multinomial models to continuous-time multidimensional diffusion models for contingent claims prices. The key to the approach is to approximate the $$N$$-dimensional diffusion price process by a sequence of $$N$$-variate, $$(N+1)$$-nomial processes. It is shown that contingent claims prices and dynamic replicating portfolio strategies derived from the discrete time models converge to their corresponding continuous-time limits.