Pricing cross-currency interest rate swaps under the Levy market model

This paper derives a pricing model for interest rate swaps when the underlying markets and settlement currency can be set arbitrarily. Using the risk-neutral valuation method developed by Musiela and Rutkowski (Martingale methods in financing modelling, 2nd edn, Springer, New York, 2005), the authors generate arbitrage-free prices for a Levy market. The Levy processes are attractive because they support better statistical fits than a Gaussian economy. A closed-form solution for the swap value results from replicating the payment at each settlement date. The results then show that the domestic and foreign term structures are important factors in the pricing model; the swap value contains a correction term that reflects the currency hedging cost for the correlation between interest rates and the exchange rate.