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
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
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