Efficient and Accurate Log-Levy Approximations of Levy-Driven LIBOR Models

Antonis Papapantoleon, John Schoenmakers, David Skovmand

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The LIBOR market model is very popular for pricing interest rate derivatives
but is known to have several pitfalls. In addition, if the model is driven by a
jump process, then the complexity of the drift term grows exponentially fast (as
a function of the tenor length). We consider a Lévy-driven LIBOR model and
aim to develop accurate and efficient log-Lévy approximations for the dynamics
of the rates. The approximations are based on the truncation of the drift term
and on Picard approximation of suitable processes. Numerical experiments for
forward-rate agreements, caps, swaptions and sticky ratchet caps show that the
approximations perform very well. In addition, we also consider the log-Lévy
approximation of annuities, which offers good approximations for high-volatility
regimes.
Original languageEnglish
JournalJournal of Computational Finance
Volume15
Issue number4
Pages (from-to)3-44
ISSN1460-1559
Publication statusPublished - 2012

Cite this

Papapantoleon, Antonis ; Schoenmakers, John ; Skovmand, David. / Efficient and Accurate Log-Levy Approximations of Levy-Driven LIBOR Models. In: Journal of Computational Finance. 2012 ; Vol. 15, No. 4. pp. 3-44.
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abstract = "The LIBOR market model is very popular for pricing interest rate derivativesbut is known to have several pitfalls. In addition, if the model is driven by ajump process, then the complexity of the drift term grows exponentially fast (asa function of the tenor length). We consider a L{\'e}vy-driven LIBOR model andaim to develop accurate and efficient log-L{\'e}vy approximations for the dynamicsof the rates. The approximations are based on the truncation of the drift termand on Picard approximation of suitable processes. Numerical experiments forforward-rate agreements, caps, swaptions and sticky ratchet caps show that theapproximations perform very well. In addition, we also consider the log-L{\'e}vyapproximation of annuities, which offers good approximations for high-volatilityregimes.",
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Efficient and Accurate Log-Levy Approximations of Levy-Driven LIBOR Models. / Papapantoleon, Antonis ; Schoenmakers, John ; Skovmand, David.

In: Journal of Computational Finance, Vol. 15, No. 4, 2012, p. 3-44.

Research output: Contribution to journalJournal articleResearchpeer-review

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AU - Schoenmakers, John

AU - Skovmand, David

PY - 2012

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N2 - The LIBOR market model is very popular for pricing interest rate derivativesbut is known to have several pitfalls. In addition, if the model is driven by ajump process, then the complexity of the drift term grows exponentially fast (asa function of the tenor length). We consider a Lévy-driven LIBOR model andaim to develop accurate and efficient log-Lévy approximations for the dynamicsof the rates. The approximations are based on the truncation of the drift termand on Picard approximation of suitable processes. Numerical experiments forforward-rate agreements, caps, swaptions and sticky ratchet caps show that theapproximations perform very well. In addition, we also consider the log-Lévyapproximation of annuities, which offers good approximations for high-volatilityregimes.

AB - The LIBOR market model is very popular for pricing interest rate derivativesbut is known to have several pitfalls. In addition, if the model is driven by ajump process, then the complexity of the drift term grows exponentially fast (asa function of the tenor length). We consider a Lévy-driven LIBOR model andaim to develop accurate and efficient log-Lévy approximations for the dynamicsof the rates. The approximations are based on the truncation of the drift termand on Picard approximation of suitable processes. Numerical experiments forforward-rate agreements, caps, swaptions and sticky ratchet caps show that theapproximations perform very well. In addition, we also consider the log-Lévyapproximation of annuities, which offers good approximations for high-volatilityregimes.

M3 - Journal article

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