Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities

@article{Phelan2020PricingMF,
  title={Pricing methods for $\alpha$-quantile and perpetual early exercise options based on Spitzer identities},
  author={Carolyn E. Phelan and Daniele Marazzina and Guido Germano},
  journal={Quantitative Finance},
  year={2020},
  volume={20},
  pages={899 - 918}
}
We present new numerical schemes for pricing perpetual Bermudan and American options as well as α-quantile options. This includes a new direct calculation of the optimal exercise boundary for early-exercise options. Our approach is based on the Spitzer identities for general Lévy processes and on the Wiener–Hopf method. Our direct calculation of the price of α-quantile options combines for the first time the Dassios–Port–Wendel identity and the Spitzer identities for the extrema of processes… Expand
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