Motivated by the work of P. Hagen and A. Lesniewski, an extension of the Libor market model with SABR-style stochastic volatility is studied in this thesis. Approximate solutions of forward Libor and swap rates are derived by means of low-noise expansion and the calibration approach of matching swaption implied SABR parameters is specified more precisely. In particular, approximations of SABR implied volvol and correlation parameters are suggested and the approximation of implied mean-square swap rate volatility proposed by P. Hagen and A. Lesniewski is derived in more detail. In an empirical study, the mean-square volatility approximation is compared with an approximation proposed by R. Rebonato and R. White as well with a simple freezing approximation. While the freezing approximation is only sensitive to correlation among forward rates, the Rebonato/White approximation also considers correlation among volatilities and the Hagen/Lesniewski approximation additionally accounts for correlation between rates and volatilities.
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Motivated by the work of P. Hagen and A. Lesniewski, an extension of the Libor market model with SABR-style stochastic volatility is studied in this thesis. Approximate solutions of forward Libor and swap rates are derived by means of low-noise expansion and the calibration approach of matching swaption implied SABR parameters is specified more precisely. In particular, approximations of SABR implied volvol and correlation parameters are suggested and the approximation of implied mean-square swa...
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