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PICARD APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATION TO LIBOR MODELS (2010)
| Citations: | 3 - 3 self |
BibTeX
@MISC{Papapantoleon10picardapproximation,
author = {Antonis Papapantoleon and David Skovmand},
title = {PICARD APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS AND APPLICATION TO LIBOR MODELS},
year = {2010}
}
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Abstract
The aim of this work is toprovide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochastic differential equations of the successive LIBOR rates but the methods are generally slow. Our contribution is twofold. Firstly, we propose an alternative approximation scheme based on Picard iterations. This approach is similar in accuracy to the Euler discretization, but with the feature that each rate is evolved independently of the other rates in the term structure. This enables simultaneous calculation ofderivativeprices of different maturities using parallel computing. Secondly, the product terms occurring in the drift of a LIBOR market model driven by a jump process grow exponentially as a function of the number of rates, quickly rendering the model intractable. We reduce this growth from exponential to quadratic using truncated expansions of the product terms. We include numerical illustrations of the accuracy and speed of our method pricing caplets, swaptions and forward rate agreements.
Keyphrases
libor market model product term jump process grow monte carlo pricing stochastic differential equation successive libor rate truncated expansion accurate approximation scheme term structure standard method forward rate agreement method pricing caplets different maturity picard iteration numerical illustration euler discretization alternative approximation scheme simultaneous calculation ofderivativeprices
