In this paper we study the asymptotic properties of the canonical plug-in estimates for law-invariant coherent risk measures. Under rather mild conditions not relying on the explicit representation of the risk measure under consideration, we rst prove a central limit theorem for independent...

We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel...

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...

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 jump-diffusion Libor model with jumps in a high-dimensional space (Rm) and test a stable non-parametric calibration algorithm which takes into account a given local covariance structure. The algorithm returns smooth and simply structured Lévy densities, and penalizes...

In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particularly useful for problems with a highdimensional state space and complex dependence structure of the underlying Markov process with...

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...

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. Applying the sample space with payoffs at the optimal...

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...

We consider the problem of estimating the fractional order of a L´evy 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...