Article2009

Linking caplets and swaptions prices in the LMM-SABR model

23 citations0/0 files storedThe Journal of Computational Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

ABSTRACT We use (and improve upon) a recent time-homogeneous extension of the stochastic alpha beta rho (SABR)-LIBOR market model (LMM) approach described in Rebonato (2007) to develop a quick and accurate analytical approximation to the implied swaption prices given the forward-rate SABR-LMM parameters. This approximation can be used for studies of calibration of a forward-rate-based LMM-SABR model to (portions of) the swaption matrix, to determine the constant maturity swap (CMS) drift corrections (see Hagan (2003)) and to study the congruence between the caplet and swaption markets.

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References

1997The Market Model of Interest Rate Dynamics 2001Interest Rate Models Theory and Practice 1997LIBOR and swap market models and measures 2006Moment explosions in stochastic volatility models 2000Volatility skews and extensions of the Libor market model 2000Forward Rate Volatilities, Swap Rate Volatilities, and Implementation of the LIBOR Market Model 2012Volatility and Correlation 2003A displaced-diffusion stochastic volatility LIBOR market model: motivation, definition and implementation

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