Efficient Evaluation of Expectations of Functions of a Lévy Process and Its Extremum
Efficient Evaluation of Expectations of Functions of a Lévy Process and Its Extremum
We prove simple general formulas for expectations of functions of a Lévy process and its running extremum. Under additional conditions, we derive analytical formulas using the Fourier/Laplace inversion and Wiener-Hopf factorization, and discuss efficient numerical methods for realization of these formulas. As applications, the cumulative probability distribution function of the …