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| An Asymptotic FX Option Formula in the Cross Currency Libor Market Model: Wilmott Magazine Article |
| Atsushi Kawai & Peter Jäckel |
508 Views |
In this article, we introduce analytic approximation formulae for FX options in the Libor market model (LMM). The method to derive the formulae is an asymptotic expansion
technique introduced in Kawai [Kaw03].
We first apply the method to the lognormal LMM and lognormal FX model. Then, the method is applied to the displaced diffusion LMM and the displaced diffusion FX model. Some numerical examples show that the derived formulae are sufficiently accurate for practical applications.
[First published in issue 28 of Wilmott - March 2007] |
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| Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance |
| Eric A. Forgy |
3969 Views |
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The present report contains an introduction to some elementary concepts in non- commutative differential geometry. The material extends upon ideas first presented by Dimakis and M. Muller-Hoissen. In particular, stochastic calculus and the Ito formula are shown to arise naturally from introducing noncommutativity of functions (0-forms) and differentials (1-forms). The abstract construction allows for the straightforward generalization to lattice theories for the direct implementation of numerical models. As an elementary demonstration of the formalism, the standard Black-Scholes model for option pricing is reformulated.
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| Funds Transfer Pricing within Bank Asset-Liability Management - 24 & 25 June 2013 - Central London - 10% Discount |
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Quote VIP Code: FKM62583WLT to receive your 10% discount |
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