Term structure modelling for multiple curves with stochastic discontinuities

Abstract

The goal of the paper is twofold. On the one hand, we develop the first term structure framework which takes stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. On the other hand, we provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework. In this setting, we characterize absence of arbitrage by means of NAFLVR and provide a fundamental theorem of asset pricing for multiple curve markets. The approach with stochastic discontinuities permits to embed market models directly, thus unifying seemingly different modeling philosophies. We also develop a new tractable class of models, based on affine semimartingales, going beyond the classical requirement of stochastic continuity. Due to the generality of the setting, the existing approaches in the literature can be embedded as special cases.Date: July 24, 2019. 2010 Mathematics Subject Classification. 60G44, 60G57, 91G20, 91G30. JEL classification: C02, C60, E43, G12.

Arbitrage-free Nelson–Siegel model for multiple yield curves

“…We then have the following definition of a multiple curve financial market (compare [4,13]). Definition 3 For a fixed time horizon T < ∞ we consider a financial market consisting of the following basic traded assets 1.…”

Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework

“…While Beleza Sousa et al (2014) calibrated solely zero-coupon log-bond prices, from which one is not able to construct a post-crisis multi-curve interest rate market, we calibrate zero-coupon log-bond prices and log-δ-bond prices on top in order to encompass forward rate agreements and to be conform with the multi-curve framework (cf. Fontana et al (2020) for the notion of δ-bonds). The modeling of log-δ-bond prices allows building forward-rate-agreements (FRAs) so that we have the basic building blocks for multi-curve interest rate markets.…”

“…The detailed mechanism in the multi-curve markets is quite involved, and we refer Fontana et al (2020) for a precise description. Intuitively, traded instruments are forward-rate agreements which exchange a fixed premium against a floating rate over a future time interval [T, T + δ].…”

“…While before the crisis, the curves were independent of δ, after the crisis the tenure can no longer be neglected. The authors of Fontana et al (2020) showed that forward-rate agreements can be decomposed into δ-bonds, which we denote by P(t, T, δ). If δ = 0 we write P(t, T) = P(t, T, 0), which is the single-curve case considered previously.…”

“…The literature on multiple yield curves is manifold and we refer to the works of Grbac and Runggaldier (2015) and Henrard (2014) for an overview. The general theory and affine models have been developed and applied, among others, in Cuchiero et al (2016Cuchiero et al ( 2019; Fontana et al (2020); ; Mercurio (2010).…”