Arbitrage-free pricing of American options in nonlinear markets
Abstract
We re-examine and extend the findings from the recent paper by Dumitrescu, Quenez and Sulem (2018) who studied American and game options in a particular market model using the nonlinear arbitrage-free pricing approach developed in El Karoui and Quenez (1997). In the first part, we provide a detailed study of unilateral valuation problems for the two counterparties in an American-style contract within the framework of a general nonlinear market. We extend results from Bielecki and Rutkowski (2015) and Bielecki, Cialenco and Rutkowski (2018) who examined the case of a European-style contract. In the second part, we present a BSDE approach, which is used to establish more explicit pricing, hedging and exercising results when solutions to reflected BSDEs have additional desirable properties.
Keywords
Cite
@article{arxiv.1804.10753,
title = {Arbitrage-free pricing of American options in nonlinear markets},
author = {Edward Kim and Tianyang Nie and Marek Rutkowski},
journal= {arXiv preprint arXiv:1804.10753},
year = {2018}
}