Groupe d’études et de recherche en analyse des décisions

# Numerical Pricing of Contingent Claims on Multiple Assets and/or Factors - A Low-Discrepancy Markov Chain Approach

## Jin-Chuan Duan, Geneviève Gauthier et Jean-Guy Simonato

We develop a Markov chain pricing method capable of handling several state vari- ables. The Markov chain construction of Duan and Simonato (2000) is modified so that higher-dimensional valuation problems can be dealt with. Their design relies on a Cartesian product, which grows in a power fashion as the number of assets/factors increases. We use a multi-dimensional low-discrepancy sequence as the building block for constructing the Markov chain in order to take advantage of the high degree of uniformity inherent in such sequences. Our design contains two critical components. First, we have devised a way of computing analytically the entries of the transition probability matrix and then shown that such a Markov chain converges weakly to the target Markov process. Second, we have utilized an elliptical restriction as a way of removing non-critical components of the Markov chain to enhance the computational efficiency. Numerical examples are provided.

, 25 pages