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Pricing Swaptions Under the LIBOR Market Model of Interest Rates with Local-Stochastic Volatility Models

Wilmott, Vol. 2012, No. 61, 2012

31 Pages Posted: 18 Apr 2010 Last revised: 12 Jan 2013

Kenichiro Shiraya

Mizuho-DL Financial Technology Co., Ltd.

Akihiko Takahashi

University of Tokyo - Faculty of Economics

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: April 9, 2010

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.

Keywords: Asymptotic Expansion, Local Volatility, Affine-type Stochastic Volatility, Libor Market Model, Approximation Formula

Suggested Citation

Shiraya, Kenichiro and Takahashi, Akihiko and Yamazaki, Akira, Pricing Swaptions Under the LIBOR Market Model of Interest Rates with Local-Stochastic Volatility Models (April 9, 2010). Wilmott, Vol. 2012, No. 61, 2012. Available at SSRN: https://ssrn.com/abstract=1591482

Kenichiro Shiraya

Mizuho-DL Financial Technology Co., Ltd. ( email )

Japan

Akihiko Takahashi (Contact Author)

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033
Japan

Akira Yamazaki

Hosei University - Graduate School of Business Administration ( email )

Japan

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