The Amin/Bodurtha Framework For Interest Rate And Exchange Rate Derivatives - Implementation and Application

The Amin and Bodurtha (1995) framework, building on a discrete-time version of the Heath, Jarrow, and Morton (1992) term structure model and the binomial model of Cox, Ross, and Rubinstein (1979), allows a consistent valuation of instruments driven by three sources of uncertainty: domestic interest rate risk, foreign interest rate risk and exchange rate risk. This makes the framework applicable to a large number of different products, such as currency swap options, currency warrants, currency exchange warrants or differential/cross-rate swaps to name just a few. The very general nature of the Amin/Bodurtha framework, however, requires for its practical application further specifications and, based on this, the computation of the model’s drift term to build the tree. We propose a directly implementable model within the Amin and Bodurtha (1995) framework which allows, in spite of its parsimonious nature, any combination of up and down moves of the three factors under consideration without restraining volatility functions or correlations of the three processes. An efficiency analysis shows the gain in terms of computing time by the use of our model compared to a more general model with the same number of nodes and the same probabilities. In addition, we modify the three-factor Amin/Bodurtha framework to obtain a two-factor framework able to price equity-linked and commodity-linked interest rate derivatives (such as callable Brady bonds or Long-Term Equity Anticipation Securities). For this, we compute the drift rates, establish a related parsimonious model specification and perform an efficiency analysis similar to that for the original Amin/Bodurtha framework.