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Lithuanian Mathematical Journal

, Volume 59, Issue 3, pp 338–356 | Cite as

Minimal variance hedging in multicurve interest rate modeling

  • Markus Hess
Article

Abstract

We consider minimal variance hedging in a pure-jump multicurve interest rate model. In the first part, we derive arithmetic multifactor martingale representations for the spread, OIS, and LIBOR rate, which are bounded from below by a real-valued constant. In the second part, we investigate minimal variance hedging and provide a closed-form formula for the related minimal variance portfolio. We apply this result to several examples covering both replicable and nonreplicable claims. We conclude the paper with a consideration of delta hedging.

Keywords

multicurve model OIS rate LIBOR rate basis spread minimal variance hedging delta hedge wealth process self-financing portfolio replicable claim arithmetic multifactor model Ornstein–Uhlenbeck process jump process Malliavin calculus Clark–Ocone formula 

MSC

60G44 60G51 60H07 60H10 91B30 91B70 

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Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Markus Hess
    • 1
  1. 1.Frankfurt/MainGermany

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