An Arithmetic Pure-Jump Multi-Curve Interest Rate Model

International Journal of Theoretical and Applied Finance (IJTAF), Forthcoming

28 Pages Posted: 4 Aug 2016 Last revised: 23 Oct 2019

See all articles by Markus Hess

Markus Hess

Université Libre de Bruxelles (ULB)

Date Written: October 4, 2019

Abstract

We propose an innovative multi-curve model involving interest rates and (ordered) spreads which are modeled by arithmetic martingale processes being larger than some arbitrarily chosen constant. Under our mean-reverting pure-jump approach, we derive tractable martingale representations for the OIS rate, the spread as well as the LIBOR rate and provide analytical caplet price formulae. In a second part, we introduce an extended jump-diffusion version of our model and investigate hedging and the computation of Greeks under this new specification. As a by-product, we infer the related arithmetic pure-jump single-curve model. We finally consider the modeling of future information in multi-curve interest rate markets by enlarged filtrations and deduce the related OIS and LIBOR rate representations as well as the corresponding information premium.

Keywords: stochastic calculus; Ornstein-Uhlenbeck process; arithmetic multi-factor model; pure-jump process; multi-curve model; OIS rate; LIBOR rate; basis spread; forward measure; caplet/floorlet pricing; hedging; Greeks; inverse Fourier pricing; enlarged filtration; future information; insider trading

JEL Classification: G12, D52

Suggested Citation

Hess, Markus, An Arithmetic Pure-Jump Multi-Curve Interest Rate Model (October 4, 2019). International Journal of Theoretical and Applied Finance (IJTAF), Forthcoming. Available at SSRN: https://ssrn.com/abstract=2817816 or http://dx.doi.org/10.2139/ssrn.2817816

Markus Hess (Contact Author)

Université Libre de Bruxelles (ULB) ( email )

CP 210 Boulevard du Triomphe
Brussels, Brussels 1050
Belgium

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