In this paper, we propose a Weighted Stochastic Mesh (WSM) algorithm for approximating the value of discrete- and continuous-time optimal stopping problems. In this context, we consider tractability of such problems via a useful notion of semitractability and the introduction of a tractability...

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 propose a Libor model with a high-dimensional speciallystructured system of driving CIR volatility processes. A stablecalibration procedure which takes into account a given local correlationstructure is presented. The calibration algorithm is FFT based, so fastand easy to implement.

A new algorithm for finding value functions of finite horizon optimal stopping problems in one-dimensional diffusion models is presented. It is based on a time discretization of the corresponding integral equation. The proposed iterative procedure for solving the discretized integral equation...

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

In this paper we propose a jump-diffusion Libor model with jumps in ahigh-dimensional space (R^m) and test a stable non-parametric calibrationalgorithm which takes into account a given local covariance structure.The algorithm returns smooth and simply structured Lévy densities, andpenalizes the...

The calibration of financial models has become rather important topic in recent years mainly because of the need to price increasingly complex options in a consistent way. The choice of the underlying model is crucial for the good performance of any calibration procedure. Recent empirical...

We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit...