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1 Crédit Agricole

Abstract : In this work we derive new analytical weak approximations for arithmetic means of geometric Brownian motions using a scalar log-normal Proxy with an averaged volatility. The key features of the approach are to keep the martingale property for the approximations and to provide new integration by parts formulas for geometric Brownian motions. Besides, we also provide tight error bounds using Malliavin calculus, estimates depending on a suitable dispersion measure for the volatilities and on the maturity. As applications we give new price and implied volatility approximation formulas for basket call options. The numerical tests reveal the excellent accuracy of our results and comparison with the other known formulas of the literature show a valuable improvement.

Keywords : Weak approximation Geometric Brownian motion Arithmetic mean Malliavin calculus Basket options





Autor: Romain Bompis -

Fuente: https://hal.archives-ouvertes.fr/



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