A Multiple Curve Lévy Swap Market Model

ABSTRACT

In this paper, we develop an arbitrage-free multiple curve model through the specification of forward swap rates. Two sets of assets are chosen as fundamentals: OIS zero-coupon bonds and forward rate agreements. This is a very natural approach since, on the one hand, OIS bonds represent the class of risk-free discount bonds and, on the other hand, the mid and long maturity part of the interest rate term structure is bootstrapped from quotes of swap rates that can be represented by FRA rates and OIS bond prices in the multiple curve setting. We construct the rates via a backward induction along the tenor structure on the basis of the forward swap measures. Time-inhomogeneous Lévy processes are used as drivers of the dynamics. As an application, we derive an approximative Fourier-based valuation formula for swaptions. The model is implemented and calibrated by using generalized hyperbolic Lévy processes as drivers.

KEYWORDS:

• multiple curve model
• swap market model
• Lévy processes
• swaption pricing

Acknowledgments

Eva Lütkebohmert gratefully acknowledges the financial support by the German Research Foundation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the German Research Foundation through the project [LU1186/4-1].