Valuing three-asset barrier options and autocallable products via exit probabilities of Brownian bridge

This paper discusses pricing barrier options and autocallable structured products on underlying three assets via exit probabilities of a three-dimensional Brownian bridge. We derive the formulas for marginal and bivariate co-exit probability. Despite the impossibility of finding an analytical trivariate co-exit probability, its calculation is not regarded as a purely numerical problem. After specifying the component to be numerically evaluated, logistic regression with the Monte Carlo method is adopted to predict it. Extensive numerical experiments of calculating the exit probability of the three-dimensional Brownian motion and pricing complex products demonstrate the effectiveness and efficiency of our approach.