Risk-Managing Bermudan Swaptions in a LIBOR Model

Abstract

Estimating the sensitivity of swaption values to volatility changes is tricky, because there are many different ways the volatility function may be deformed that give rise to the same change in overall variance. The authors show how a standard recalibration based on perturbing forward rate volatilities and simulating the changes in swaption values the “time homogeneous forward rate volatility” approach can lead to substantial uncertainty in swap vegas. They propose an alternative technique based on time homogeneity of swap rate volatility, which performs much better because it distributes the effect of the perturbation more smoothly across maturities. This allows more accurate swap vega estimates using many fewer Monte Carlo runs.