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

18 Pages Posted: 8 Oct 2015

See all articles by Wolfram Boenkost

Wolfram Boenkost

Lucht Probst Associates GmbH

Wolfgang M. Schmidt

Frankfurt School of Finance & Management

Date Written: November 7, 2014

Abstract

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.

Keywords: interest rate modelling, volatility smile/skew, Libor market model, Markov functional model, potential future exposure, counterparty default

JEL Classification: G13

Suggested Citation

Boenkost, Wolfram and Schmidt, Wolfgang M., A Functional Libor Market Model: Implementation and Application to Exposure Measurement (November 7, 2014). Available at SSRN: https://ssrn.com/abstract=2671146 or http://dx.doi.org/10.2139/ssrn.2671146

Wolfram Boenkost

Lucht Probst Associates GmbH ( email )

Grosse Gallusstr. 9
Frankfurt, 60311
Germany

HOME PAGE: http://www.l-p-a.com

Wolfgang M. Schmidt (Contact Author)

Frankfurt School of Finance & Management ( email )

Adickesallee 32-34
Frankfurt am Main, 60322
Germany

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