Pricing Swaptions under the Libor Market Model of Interest Rates with Local-Stochastic Volatility Models

Kenichiro Shiraya, Akihiko Takahashi and Akira Yamazaki
Additional contact information
Kenichiro Shiraya: Mizuho-DL Financial Technology Co.,Ltd.
Akihiko Takahashi: Faculty of Economics, University of Tokyo
Akira Yamazaki: Mizuho-DL Financial Technology Co.,Ltd.

No CARF-F-255, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: This paper presents a new approximation formula for pricing swaptions and caps/floors under the LIBOR market model of interest rates (LMM) with the local and affine-type stochastic volatility. In particular, two approximation methods are applied in pricing, one of which is so called "drift-freezing" that fixes parts of the underlying stochastic processes at their initial values. Another approximation is based on an asymptotic expansion approach. An advantage of our method is that those approximations can be applied in a unified manner to a general class of local-stochastic volatility models of interest rates. To demonstrate effectiveness of our method, the paper takes CEVHeston LMM and Quadratic-Heston LMM as examples; it confirms sufficient flexibility of the models for calibration in a caplet market and enough accuracies of the approximation method for numerical evaluation of swaption values under the models.

Pages: 32 pages
Date: 2011-10
New Economics Papers: this item is included in nep-ore
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