Stochastic interest rate modelling using a single or multiple curves: an empirical performance analysis of the Lévy forward price model

Abstract

In current financial markets negative interest rates have become rather persistent, while in theory it is often common practice to discard such rates as incredible and irrelevant. However, from a risk management perspective, it is crucially important to financial institutions to properly account for this phenomenon in their Asset Liability Management (ALM) studies. In this paper, we develop a coherent framework on how to best incorporate negative interest rates in these studies through a single curve stochastic term structure model and compare it to its multiple curve analogue. It turns out that, from the wide range of available single curve models, especially the Lévy Forward Price model (LFPM) of Eberlein and Özkan [The Lévy LIBOR model. Financ. Stoch., 2005, 9, 327-348] seems appropriate for ALM purposes. This paper describes an optimisation routine for calibrating this LFPM under the risk-neutral measure in both the single and multiple curve framework to the market prices of interest rate caplets with different strike rates, maturities and tenors. In addition, an empirical performance analysis is made of the single and multiple curve LFPM, where we include four deterministic volatility specifications and provide an explicit parametrisation of a piecewise homogeneity restriction with both deterministic and random breakpoints. This comparative analysis indicates that both the single and multiple curve LFPM is best adopted with the Linear-Exponential Volatility (LEV) specification and that deterministic breakpoints should be included, rather than random breakpoints.

Interest Rate Modelling in the Presence of Discontinuities and its Sensitivities

“…Wang et al (2017) proposed pricing of vulnerable American option under jump-diffusion process, whereas Jiahui et al (2019) obtained a closed form evaluation formula for that of European option having credit and jump risks under inadequate information. Perelló et al (2020) focused on stochastic interest rate modelling for assessing future with ramification in climate change, while Verschuren (2020) developed a coherent structure on how to include certain interest rates in a single curve stochastic term structure model and did comparison with multiple curve analogue.…”