Variance Reduction Techniques for Large Scale Risk Management
We describe several variance reduction techniques that we implemented to accelerate the convergence of Monte Carlo simulation for the pricing of a portfolio of mortgages. The main requirement was to price each mortgage individually. Since mortgage portfolios are very large in practice, the number of samples was kept low (under 2000) in order to price a portfolio in a reasonable amount of time. Part of the approach was to evaluate various low-discrepancy sequences and Brownian bridge constructions to generate Brownian motion. We also developed original algorithms for two types of conventional variance reduction techniques: control variates and importance sampling. Both algorithms are adaptive, i.e. they extract information on the portfolio from previous Monte Carlo runs in order to tune some of the parameters contained in the algorithms. We describe how to reduce the dimensionality of the problem in order to apply these techniques successfully.
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