Quasi-Monte Carlo in Tree Pricing Models

Abstract

Quasi-Monte Carlo sampling methods for the pricing of path dependent derivatives have been shown to outperform random sampling when used in a variety of different interest rate models. In certain applications it is desirable to perform Monte Carlo simulations on a tree based interest rate model, however there is a lack of literature describing how to perform QMC on a tree. This paper describes a path compensation algorithm that allows QMC sampling based on the Sobol sequence in tree pricing applications. Solutions are provided for single factor Hull-White trinomial trees as well as the Black- Karasinski model. This algorithm can be adapted to binomial tree models. Path construction by the Brownian bridge is compared to a fast discrete cosine transform (DCT) approximation of principal component analysis (PCA). Both QMC methods are shown to outperform MC.

Keywords: PCA, QMC, Sobol

JEL Classification: C15