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dc.contributor.authorBayer, Christian
dc.contributor.authorTempone, Raul
dc.contributor.authorWolfers, Sören
dc.date.accessioned2019-01-13T09:46:22Z
dc.date.available2019-01-13T09:46:22Z
dc.date.issued2018-09-20
dc.identifier.urihttp://hdl.handle.net/10754/630806.1
dc.description.abstractWe present a novel method for the numerical pricing of American options based on Monte Carlo simulation and optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called optimal \emph{exercise regions}, which consist of points in time and space at which the option is exercised. In contrast, our method determines \emph{exercise rates} of randomized exercise strategies. We show that the supremum of the corresponding stochastic optimization problem provides the correct option price. By integrating analytically over the random exercise decision, we obtain an objective function that is differentiable with respect to perturbations of the exercise rate even for finitely many sample paths. Starting in a neutral strategy with constant exercise rate then allows us to globally optimize this function in a gradual manner. Numerical experiments on vanilla put options in the multivariate Black--Scholes model and preliminary theoretical analysis underline the efficiency of our method both with respect to the number of time-discretization steps and the required number of degrees of freedom in the parametrization of exercise rates. Finally, the flexibility of our method is demonstrated by numerical experiments on max call options in the Black--Scholes model and vanilla put options in Heston model and the non-Markovian rough Bergomi model.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/abs/1809.07300
dc.titlePricing American Options by Exercise Rate Optimization
dc.typePreprint
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.institutionWeierstrass Institute for Applied Analysis and Stochastic s (WIAS)
dc.identifier.arxivid1809.07300
refterms.dateFOA2019-01-13T09:46:23Z


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