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An Arithmetic Pure-Jump Multi-Curve Interest Rate Model

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  • MARKUS HESS

    (Independent Researcher, Frankfurt/Main, Germany)

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.

Suggested Citation

  • Markus Hess, 2019. "An Arithmetic Pure-Jump Multi-Curve Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-30, December.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:08:n:s0219024919500420
    DOI: 10.1142/S0219024919500420
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    References listed on IDEAS

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