The Integrated Edgeworth Expansion

A series expansion approach to approximate the exercise probabilities has been previously used e.g. by Jarrow and Rudd [44], Turnbull and Wakeman [72], Ju [47] and Collin-Dufresne, Goldstein [19]. A main drawback of their approach is the dependency of the series expansion on the underlying dynamics of the random variables. This makes the application of their series expansion approach very uncomfortable and intractable for a wider practical use. 

With the lEE algorithm we eliminate this main drawback and derive a model independent approximation scheme in the sense that the model spe- 

In option pricing theory, we are usually not interested in a method for the approximation of an unknown pdf. Typically, there is a need for a practicable method to eompute the (exereise) probabilities 

Therefore, we derive an integrated form of the generalized EE by eomput-ing the integral in closed-form ending up with a tractable solution similar to section (3)). First of all, we show that the integral 

to prove the existence of the above integral we have to show that the integral 

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Therefore, we term this generalized series expansion the Integrated Edgeworth Expansion (lEE). The EE originally is derived to approximate density functions instead of probabilities. 

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