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.
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 language | English |
|---|---|
| Journal | Journal of Computational Finance |
| Volume | 15 |
| Issue number | 4 |
| Pages (from-to) | 3-44 |
| ISSN | 1460-1559 |
| Publication status | Published - 2012 |
Cite this
Papapantoleon, A., Schoenmakers, J., & Skovmand, D. (2012). Efficient and Accurate Log-Levy Approximations of Levy-Driven LIBOR Models. Journal of Computational Finance, 15(4), 3-44. http://www.risk.net/digital_assets/5397/jcf_shoenmakers_web.pdf