# Efficient inverse Z-transform and pricing barrier and lookback options with discrete monitoring

@article{Boyarchenko2022EfficientIZ, title={Efficient inverse Z-transform and pricing barrier and lookback options with discrete monitoring}, author={Svetlana Boyarchenko and Sergei Levendorskii}, journal={ArXiv}, year={2022}, volume={abs/2207.02858} }

. We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse Z -transform, 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 process and its running maximum and the price of the option to exchange the power of a stock…

## One Citation

### Efficient Evaluation of Double-Barrier Options and Joint CPDF of a Levy Process and Its Two Extrema

- MathematicsSSRN Electronic Journal
- 2022

In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Lévy models; the calculations are in the dual space, and the…

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