A Functional Libor Market Model: Implementation and Application to Exposure Measurement

Evaluating interest rate derivatives stands and falls by a model properly capturing the volatility smile/skew. This does not only apply to pricing but also to evaluating counterparty default charges. We propose an arbitrage free model where forward Libor rates from the standard Libor Market Model (LMM) are transformed by an appropriate functional to reproduce the volatility structure in the cap market. Implementing the model is easy, efficient and stays as closely as possible to the standard LMM implementation. It combines both flexibility and factorness of the LMM and perfect consistency with the smile/skew. Calibration examples demonstrate the accuracy of the smile/skew calibration. Applications highlight the sensitivity of counterparty exposure measurement with respect to the volatility structure in the market.