About Long-Term Cross-Currency Bermuda Swaption Pricing

Abstract

This paper details first the pricing process of a Bermuda swaption and, in a second step, the pricing of a cross-currency Bermuda swaption from a computational point of view. Our aim is to examine the lengthy process that provides a Bermuda swaption price with special attention to the tests used for assessing the coherence of the price. We only consider long-term derivatives that lead to issues related to missing data and require calibration adjustment. We also deal with the sensitivity of the cross-currency swaption price to the choice of model. The standard model to price this kind of options is a 3-factors hybrid model based on the Libor Market Model that typically combines the domestic market, the foreign market and the foreign exchange market. We study the impact of each one of these stochastic factors on the price of a long-term cross-currency Bermuda swaption. In particular, this study illustrates the relation between the cross-currency product and the volatility of each one of the three markets involved (domestic, foreign and the foreign exchange market).