Asian option approximation

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The procedure is the following: The approximating density for is given by the following expression: For this reason Turnbull and Wakeman [ 33 ] and Ritchken and al. ACM 15, 1 January, The maximum error committed with a ME approach with four moments is equal at 0. In section 1 we describe the Black-Scholes framework underlying the Asian option problem. However, in the computation above it is preferable to use numerical integration.

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Obviously this approximation has the limit that there is no expression for bounding the error and moreover it is not guaranteed the positivity of the density, but respect to the Edgeworth expansion around a lognormal distribution the current approximation appears much more robust.

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For this reason Turnbull and Wakeman [ 33 ] and Ritchken and al. Milevsky and Posner [ 25 ] state also that, according to the Kolmogorov-Smirnov criterion, this density is a better fit to the true density than the lognormal, where the true density has been estimated using Monte Carlo simulation. Two features of the method are: In Fusai and Tagliani [ 14 ] are discussed three possible choices: E 0 Yes Edgeworth Yes simple; good accuracy; no error bound. This fact should discourage from using an Edgeworth approximation when the distribution is not uniquely determined by its moments.

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