Bermudan Swaption Pricing and Calibration Based on Libor Market Model

SONG Bin,WANG Siyan

Journal of Systems Science and Mathematical Sciences ›› 2018, Vol. 38 ›› Issue (3) : 334-347.

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Journal of Systems Science and Mathematical Sciences ›› 2018, Vol. 38 ›› Issue (3) : 334-347. DOI: 10.12341/jssms13385

Bermudan Swaption Pricing and Calibration Based on Libor Market Model

  • SONG Bin ,WANG Siyan
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Abstract

Since Libor market model (LMM) is modelling the observable interest rate and avoiding the transformation process from instantaneous forward rate to market interest rate, LMM is chosen for Bermudan swaption pricing and employed Least-Squared Monte Carlo to deal with early-exercise characteristics. About the model calibration, the implied volatility of swaption in Libor market model exists closed-form solution relationship with forward Libor's volatility, which can improve the calibration's efficiency and accurancy. The paper adopts the fixed maturity European swaption to calibrate Libor market model. After the calibration, MSE between the implied volatility of European swaption and the related market quote decreases from 1198.04{\%} to 4.63{\%} and shows better calibration effect. At last, the calibrated parameters is employed for Bermudan swaption pricing and compared with the results European swaption with same strike interest rate. The results show that the Bermudan swaption's price is obviously higher than the related European swaption and validate the pricing method and calibration's correctness in some degree.

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SONG Bin , WANG Siyan. Bermudan Swaption Pricing and Calibration Based on Libor Market Model. Journal of Systems Science and Mathematical Sciences, 2018, 38(3): 334-347 https://doi.org/10.12341/jssms13385
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