Potential future exposure calculations using the BGM model



We investigate the use of the Brace–Gatarek–Musiela (BGM) model in potential future exposure (PFE) calculations for various exotic interest rate products. Monte Carlo simulation is required to generate PFE scenarios. If the pricing model is also implemented using Monte Carlo simulation, PFE calculations are exceptionally demanding, involving nested Monte Carlo simulations. To reduce computation time, we look at two approximate pricing methods—a Longstaff-Schwartz regression-based approach, and a finite difference approach using a drift approximated BGM model. Numerical results are presented for several different exotic trade types. PFE results delivered by the two approximate methods are compared with results obtained by full resimulation, i.e. nested Monte Carlo. In the test cases we looked at, both approaches produced good results and were several orders of magnitude faster than full resimulation. However, care must be taken when using the regression-based approach. In particular, results can vary significantly depending on the order of the polynomial basis functions used in the regressions. Copyright © 2009 Wilmott Magazine Ltd