Time-Changed Lévy LIBOR Market Model: Pricing and Joint Estimation of the Cap Surface and Swaption Cube

68 Pages Posted: 24 May 2012 Last revised: 22 May 2013

See all articles by Markus Leippold

Markus Leippold

University of Zurich - Department of Banking and Finance; University of Zurich - Faculty of Economics, Business Administration and Information Technology

Jacob Stromberg

Swiss Finance Institute

Date Written: May 1, 2013

Abstract

We propose a novel time-changed Lévy LIBOR market model for the joint pricing of caps and swaptions. The time changes are split into three components. The first component allows us to match the volatility term structure, the second generates stochastic volatility, and the third one accommodates for stochastic skew. The model is parsimonious, yet flexible enough to accommodate the behavior of both caps and swaptions well. For the joint estimation we use a comprehensive dataset spanning the recent financial crisis. We fi nd that, even during the recent fi nancial crisis, neither market is as fragmented as suggested by the previous literature.

Keywords: LIBOR market models, time-changed Lévy process, caps volatilities, swaption cube, unscented Kalman filter

JEL Classification: C51, E43, G13

Suggested Citation

Leippold, Markus and Stromberg, Jacob, Time-Changed Lévy LIBOR Market Model: Pricing and Joint Estimation of the Cap Surface and Swaption Cube (May 1, 2013). Swiss Finance Institute Research Paper No. 12-23. Available at SSRN: https://ssrn.com/abstract=2065375 or http://dx.doi.org/10.2139/ssrn.2065375

Markus Leippold (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

University of Zurich - Faculty of Economics, Business Administration and Information Technology ( email )

Plattenstrasse 14
Zürich, 8032
Switzerland

Jacob Stromberg

Swiss Finance Institute ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

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