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Picard Approximation of Stochastic Differential Equations and Application to Libor Models

Antonis Papapantoleon () and David Skovmand ()
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Antonis Papapantoleon: Institute of Mathematics, TU Berlin and Quantitative Products Laboratory, Deutsche Bank AG, Postal: Straße des 17. Juni 136, 10623 Berlin, Germany
David Skovmand: Aarhus School of Business and CREATES, Postal: Aarhus University, Fuglesangs Allé 4, 8210 Aarhus V, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: The aim of this work is to provide 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 of derivative prices 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.

Keywords: LIBOR models; Lévy processes; Picard approximation; drift expansion; parallel computing. (search for similar items in EconPapers)
JEL-codes: C63 G12 G13 (search for similar items in EconPapers)
Pages: 21
Date: 2010-07-16
New Economics Papers: this item is included in nep-cmp and nep-ore
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