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search.filters.applied.f.access: openAccess × Subject: Bermudan options ×

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    Optimal dual martingales and their stability; fast evaluation of Bermudan products via dual backward regression
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Schoenmakers, John G.M.; Huang, Junbo
    Literaturverz. In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options. We provide a theorem which give conditions for a martingale to be surely optimal, and a stability theorem concerning martingales which are near to be surely optimal in a sense. Guided by these theorems we develop a regression based backward construction of such a martingale in a Wiener environment. In turn this martingale may be utilized for computing upper bounds by non-nested Monte Carlo. As a by-product, the algorithm also provides approximations to continuation values of the product, which in turn determine a stopping policy. Hence, we obtain lower bounds at the same time. The proposed algorithm is pure dual in the sense that it doesn't require an (input) approximation to the Snell envelope, is quite easy to implement, and in a numerical study we show that, regarding the computed upper bounds, it is comparable with the method of Belomestny, et. al. (2009).
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    Randomized optimal stopping algorithms and their convergence analysis
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Bayer, Christian; Belomestny, Denis; Hager, Paul; Pigato, Paolo; Schoenmakers, John G. M.
    In this paper we study randomized optimal stopping problems and consider corresponding forward and backward Monte Carlo based optimization algorithms. In particular we prove the convergence of the proposed algorithms and derive the corresponding convergence rates.
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    Pricing Bermudan options by nonparametric regression : optimal rates of convergence for lower estimates
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Belomestny, Denis
    The problem of pricing Bermudan options using simulations and nonparametric regression is considered. We derive optimal non-asymptotic bounds for the low biased estimate based on a suboptimal stopping rule constructed from some estimates of the optimal continuation values. These estimates may be of different nature, they may be local or global, with the only requirement being that the deviations of these estimates from the true continuation values can be uniformly bounded in probability. As an illustration, we discuss a class of local polynomial estimates which, under some regularity conditions, yield continuation values estimates possessing the required property.