We develop an eigenfunction expansion based value iteration algorithm to solve discrete time infinite horizon optimal stopping problems for a rich class of Markov processes that are important in applications. We provide convergence analysis for the value function and the exercise boundary, and...

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator....

This paper studies subordinate Ornstein-Uhlenbeck (OU) processes, i.e., OU diffusions time changed by L\'{e}vy subordinators. We construct their sample path decomposition, show that they possess mean-reverting jumps, study their equivalent measure transformations, and the spectral representation...

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator....

We propose a new computational method for the valuation of options in jump-diffusion models. The option value function for European and barrier options satisfies a partial integro-differential equation (PIDE). This PIDE is commonly integrated in time by implicit-explicit (IMEX) time...

This paper presents a novel method to price discretely-monitored single- and double-barrier options in Levy process-based models. The method involves a sequential evaluation of Hilbert transforms of the product of the Fourier transform of the value function at the previous barrier monitoring...

We present a fast and accurate method to compute exponential moments of the discretely observed maximum of a Levy process. The method involves a sequential evaluation of Hilbert transforms of expressions involving the characteristic function of the (Esscher transformed) Levy process. It can be...