Miniworkshop on Advances in LIBOR Modeling
Organizer
JProf. Kathrin Glau
Time and Venue
Monday, 9.9.2013: 17:00 – 18:40, Room 0.01.05
Description
Interest rate modeling is a challenge from both sides, from the point of view of a practitioner as well as on the mathematical side. One reason is the complex dependence structure between rates referring to different maturities. Due to the financial crisis, a significant raise of complexity has occurred: A new market practice for discounting has established which makes the development of new models for the LIBOR rate necessary. In this session different new approaches to LIBOR modeling are discussed.
Registration
Please register for the workshop "Advances in LIBOR Modeling" using the form below. There is no additional registration fee for this workshop.
Confirmed speakers
Affine LIBOR models with multiple curves: theory, examples and calibration
by Antonis Papapantoleon
In this talk we present an extension of the LIBOR market model with stochastic basis spreads, which is developed in the spirit of the affine LIBOR models. This multiple-curve model satisfies the main no-arbitrage and market requirements (such as non-negative LIBOR-OIS spreads) already by construction. Furthermore, we clarify the connection between the affine LIBOR setup and classical LIBOR market models. The use of multidimensional affine processes as driving processes ensures the analytical tractability of the model. We provide pricing formulas for caps, swaptions and basis swaptions and discuss their efficient numerical implementation. This is joint work with Z. Grbac, J. Schoenmakers and D. Skovmand.
Additive constructions of Libor and forward price models
by Zorana Grba
In this talk we present a new approach to Libor and forward price modeling based on forward price spreads. Compared to the existing models, this additive approach automatically induces nonnegative Libor rates and at the same time is analytically tractable and flexible in the choice of the driving process. Moreover, it allows for a natural and easy extension to the multiple-curve interest rate models.
We emphasize that nonnegativity of the Libor rates does not depend on the nonnegativity of the process driving the model. This is the key flexibility of the approach, allowing for a wide class of driving processes. Brownian motion, Levy and affine processes are all included. The additive models are analytically tractable thanks to a representation of the caplet and swaption prices in terms of the forward price spreads and do not require any approximations for pricing.
We illustrate the approach by presenting a Levy specification of the model and the corresponding pricing formulas. This is joint work with K. Glau.
Construction of LIBOR models from polynomial preserving processes
by Martin Keller-Ressel
We introduce a new class of LIBOR models which satisfies at the same time the requirements of (a) being free of arbitrage (b) guaranteeing non-negative LIBOR rates, and (c) allowing for efficient pricing of single- and multi-LIBOR payoffs such as caplets, caps and swaptions. The model is based on the additive construction of non-negative martingales introduced by Glau and Grbac and uses a polynomial-preserving process as a driver. This rich class of processes includes exponential Levy processes, affine processes, quadratic Gaussian and quadratic Levy processes. In particular we discuss the efficient pricing of caps and swaptions with Fourier-methods and develop the necessary exponential transform formulae for polynomial preserving processes.
Post-Crisis Fixed Income Pricing: XIBOR Mechanics and Spreads
by Janek Gallitschke
In the wake of the financial crisis new pricing standards have emerged in the fixed income market that are inconsistent with classical interest rate models. In this talk we present a framework for pricing interest rate derivatives given the new market situation. The model is able to generate the most important stylized market features: XIBOR-OIS Spreads, Tenor Basis Spreads, and the discrepancy between FRA rates and those implied by spot XIBOR quotes.
In contrast to existing multi-curve approaches, the relevant spreads are generated endogenously from the underlying risk factors; i.e. credit and liquidity risk. We explicitly model the mechanism determining the XIBOR rate from spot quotes of individual panel banks using a reduced-form framework for the credit component. In addition, we capture liquidity risk in a structured liquidity model. Our framework thus provides a theoretical underpinning of the multi-curve approach. Finally we show how our model can be used in pricing applications. This is joint work with Stefanie Müller and Frank Thomas Seifried.