Here we develop methods for e±cient pricing multidimensional discrete-time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option...

Here we develop an approach for efficient pricing discrete-time American and Bermudan options which employs the fact that such options are equivalent to the European ones with a consumption, combined with analysis of the market model over a small number of steps ahead. This approach allows...

Here we develop methods for efficient pricing multidimensional discrete time American and Bermudan options by using regression based algorithms together with a new approach towards constructing upper bounds for the price of the option. Applying the sample space with payoffs at the optimal...

In this article we propose several pathwise and finite difference based methods for calculating sensitivities of Bermudan options using regression methods and Monte Carlo simulation. These methods rely on conditional probabilistic representations which allow, in combination with a regression...

In this paper we develop several regression algorithms for solvinggeneral stochastic optimal control problems via Monte Carlo. Thistype of algorithms is particularly useful for problems with a highdimensionalstate space and complex dependence structure of the underlyingMarkov process with...

The problem of pricing Bermudan options using Monte Carlo anda nonparametric regression is considered. We derive optimal nonasymptoticbounds for a lower biased estimate based on the suboptimalstopping rule constructed using some estimates of continuationvalues. These estimates may be of...

We consider the problem of estimating the fractional order of a L´evyprocess from low frequency historical and options data. An estimationmethodology is developed which allows us to treat both estimation andcalibration problems in a unified way. The corresponding procedureconsists of two steps:...

In this paper we carry over the concept of reverse probabilistic representations developed in Milstein, Schoenmakers, Spokoiny (2004) for diffusion processes, to discrete time Markov chains. We outline the construction of reverse chains in several situations and apply this to processes which are...

The paper focuses on the problem of pricing and hedging a European contingent claim for an incomplete market model, in which evolution of price processes for a saving account and stocks depends on an observable Markov chain. The pricing function is evaluated using the martingale approach. The...

This paper presents a new method for spatially adaptive local likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method is given a sequence of local likelihood estimates (weak estimates),...