In this paper we study simulation based optimization algorithms for solving discrete time optimal stopping problems. This type of algorithms became popular among practioneers working in the area of quantitative finance. Using large deviation theory for the increments of empirical processes, we...

We consider the problem of estimating the fractional order of a Lévy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two...

The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal nonasymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of...

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.

In this article we propose several pathwise and finite difference basedmethods for calculating sensitivities of Bermudan options using regressionmethods and Monte Carlo simulation. These methods rely on conditionalprobabilistic representations which allow, in combination with aregression...

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...