2009/07/31 by Denis Belomestny, Belomestny, Denis
Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #Mathematical Approximation and Integration #Pricing of Securities (q-fin.PR) #Statistical Methods and Inference #Stochastic processes and financial applications #q-fin.CP #q-fin.PR
paper · pdf · doi:10.48550/arxiv.0907.5599
arxiv created 2009/07/31 · openalex publication_date 2009/07/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of 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 this property.