Efficient evaluation of expectations of functions of a stable Lévy process and its extremum

09/25/2022

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by   Svetlana Boyarchenko, et al.

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Integral representations for expectations of functions of a stable Lévy process X and its supremum X̅ are derived. As examples, cumulative probability distribution functions (cpdf) of X_T, _T, the joint cpdf of X_T and _T, and the expectation of ( X_T-_T)_+, >1, are considered, and efficient numerical procedures for cpdfs are developed. The most efficient numerical methods use the conformal acceleration technique and simplified trapezoid rule.