Derivative Pricing for a Multi-curve Extension of the Gaussian, Exponentially Quadratic Short Rate Model

Abstract

The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are second order polynomials of Gaussian factor processes. This leads to an exponentially quadratic model class that is less well known than the exponentially affine class. In the latter class the factors enter linearly and for positivity one considers square root factor processes. While the square root factors in the affine class have more involved distributions, in the quadratic class the factors remain Gaussian and this leads to various advantages, in particular for derivative pricing. After some preliminaries on martingale modeling in the multi-curve setup, we concentrate on pricing of linear and optional derivatives. For linear derivatives, we exhibit an adjustment factor that allows one to pass from pre-crisis single curve values to the corresponding post-crisis multi-curve values.Keywords Multi-curve models · Short rate models · Short rate spreads · Gaussian exponentially quadratic models · Pricing of linear and optional interest rate derivatives · Riccati equations · Adjustment factors

Cross Currency Valuation and Hedging in the Multiple Curve Framework

“…This discrepancy has led to the multiple-curve framework initiated by the seminal work by Henrard [2007], and later studied by several authors, e.g. Cuchiero et al [2016] and Cuchiero et al [2019], Morini [2013], Kijima et al [2009], Kijima et al [2009], Kenyon [2010], Henrard [2010], Mercurio [2010], Mercurio [2013], Mercurio and Xie [2012], Moreni and Pallavicini [2014], Pallavicini and Tarenghi [2010], Crépey et al [2012], Grbac and Runggaldier [2015], Henrard [2014], Filipović and Trolle [2013], Grasselli and Miglietta [2016], Grbac et al [2016], Morino and Runggaldier [2014], Grbac et al [2015], Eberlein et al [2020].…”