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.
Highlights
Over the last decade, risk management practices have become increasingly emphasised in the financial sector and have become intertwined with adequate day-to-day management of financial institutions
One of the key areas where financial institutions are liable to high levels of risk and that has received a surge of attention recently, is interest rate risk management
Due to the increasing concern for negative interest rates, the underlying stochastic interest rate model should capture the prices of popular derivatives traded in the market, but allow for substantially negative interest rate scenarios as well
Summary
Risk management practices have become increasingly emphasised in the financial sector and have become intertwined with adequate day-to-day management of financial institutions. Affine short-rate models, on the other hand, are able to fully describe the dynamics of the yield curve while remaining free of arbitrage opportunities (Lemke 2006) They appear unsuited for ALM studies since we can regard them as an affine function in the short rate, even though the overall class of affine term structure models can be considered as highly general (Brigo and Mercurio 2006, Keller-Ressel et al 2013). The relevant market data on March 30th, 2012 up until April 28th, 2017 are obtained by applying a stripping procedure and the bootstrap method under the assumption of complete markets and the Efficient Market Hypothesis (EMH) From this empirical study, we conclude that the LinearExponential Volatility (LEV) specification yields, by far, the best results and outperforms the other deterministic volatility functions in both the single and multiple curve framework. The final section concludes this paper with a summary of the most important findings
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