A Dual-Curve Short Rate Model with Multi-Factor Stochastic Volatility: I. Asymptotic Analysis

30 Pages Posted: 12 Sep 2015 Last revised: 14 Jun 2016

See all articles by Andrew Lesniewski

Andrew Lesniewski

CUNY Baruch College

Heng Sun

University of Toronto

Qi Wu

City University of Hong Kong, School of Data Science

Date Written: June 9, 2016

Abstract

We present a stochastic-volatility, short rate term structure model, which extends the classic multi-factor Hull-White model. This model is designed to fit the swaption implied volatility cube and to incorporate the two-curve modeling paradigm. The model exhibits non-Gaussian forward swap rates whose distributions are parameterized across the dimensions of the volatility cube: underlying tenor, option strike and option expiration. To facilitate rapid model calibration, we establish suitable asymptotic expressions for the bond prices. Furthermore, we derive an effective SABR dynamics for each forward swap rate. Finally, we use the mean field approximation to match the effective SABR parameters corresponding to each swaption to the market levels.

Keywords: short rate models, multi-curve modeling, swaption calibration, SABR model, stochastic volatility, asymptotic expansion, mean-field approximation

Suggested Citation

Lesniewski, Andrew and Sun, Heng and Wu, Qi, A Dual-Curve Short Rate Model with Multi-Factor Stochastic Volatility: I. Asymptotic Analysis (June 9, 2016). Available at SSRN: https://ssrn.com/abstract=2634313 or http://dx.doi.org/10.2139/ssrn.2634313

Andrew Lesniewski

CUNY Baruch College ( email )

17 Lexington Avenue
New York, NY 10021
United States

Heng Sun

University of Toronto ( email )

1800 Old Meadow Rd
Apt 1114
McLean, VA 22102
United States
718-663-9666 (Phone)

Qi Wu (Contact Author)

City University of Hong Kong, School of Data Science ( email )

83 Tat Chee Avenue
Kowloon
Hong Kong

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