AN ARITHMETIC PURE-JUMP MULTI-CURVE INTEREST RATE MODEL

Markus Hess ()
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Markus Hess: Independent Researcher, Frankfurt/Main, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 08, 1-30

Abstract: We propose a multi-curve model involving interest rates and 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: Multi-curve model; OIS rate; LIBOR rate; basis spread; forward measure; caplet/floorlet pricing; hedging; Greeks; Ornstein–Uhlenbeck process; arithmetic multi-factor model; pure-jump process; enlarged filtration; future information (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500420

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