Libor model with expiry-wise stochastic volatility and displacement

TL;DR

This paper introduces a multi-factor stochastic volatility Libor model with displacement, enabling better calibration to market data and efficient pricing of caps and swaptions, even during times of market stress.

Contribution

It develops a novel Libor model with expiry-wise stochastic volatility and displacement, including affine approximations for efficient pricing and calibration.

Findings

Model calibrates well to cap and swaption market quotes.

Performs robustly during financial crises with structural volatility breaks.

Provides efficient Fourier-based pricing methods for complex derivatives.

Abstract

We develop a multi-factor stochastic volatility Libor model with displacement, where each individual forward Libor is driven by its own square-root stochastic volatility process. The main advantage of this approach is that, maturity-wise, each square-root process can be calibrated to the corresponding cap(let)vola-strike panel at the market. However, since even after freezing the Libors in the drift of this model, the Libor dynamics are not affine, new affine approximations have to be developed in order to obtain Fourier based (approximate) pricing procedures for caps and swaptions. As a result, we end up with a Libor modeling package that allows for efficient calibration to a complete system of cap/swaption market quotes that performs well even in crises times, where structural breaks in vola-strike-maturity panels are typically observed.