Efficient Control Variates and Strategies for Bermudan Swaptions in a Libor Market Model

Abstract

This paper concerns the problem of valuing Bermudan swaptions in a Libor market model. In particular we consider various efficiency improvement techniques for a Monte Carlo based valuation method. We suggest a simplification of the Andersen (2000) exercise strategy replacing a maximum over several option values by a carefully chosen single option and find it to be much more efficient. Furthermore, we test a range of control variates for Bermudan swaptions sampling the control variate at the exercise time of the Bermudan rather than at a fixed point in time. In addition, we examine the variance-bias trade-off between the numbers of outer and inner paths for the Primal-Dual simulation algorithm of Andersen (2000). We show numerically that application of these efficiency improvements in the Primal-Dual simulation algorithm - in combination with more standard antithetic variate techniques - improves both upper and lower bounds for the price estimates. Finally, we demonstrate that the presence of stochastic volatility increases the expected losses from using the simple strategy in Andersen (2000).