We study discretizations of polynomial processes using finite state Markov processes satisfying suitable moment matching conditions. The states of these Markov processes together with their transition probabilities can be interpreted as Markov cubature rules. The polynomial property allows us to...

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the asset is driven by Brownian motion, an associated "master...

Motivated by the changing nature of the natural gas industry in the European Union driven by the liberalization process, we focus on pricing of gas swing options. These options are embedded in typical gas sales agreements in the form of offtake flexibility concerning volume and time. The gas...

This paper applies to the static hedge of barrier options a technique, mean-square hedging, designed to minimize the size of the hedging error when perfect replication is not possible. It introduces an extension of this technique which preserves the computational efficiency of mean-square...

We develop a new high-performance spectral collocation method for the computation of American put and call option prices. The proposed algorithm involves a carefully posed Jacobi-Newton iteration for the optimal exercise boundary, aided by Gauss-Legendre quadrature and Chebyshev polynomial...

We develop highly-efficient parallel Partial Differential Equation (PDE) based pricing methods on Graphics Processing Units (GPUs) for multi-asset American options. Our pricing approach is built upon a combination of a discrete penalty approach for the linear complementarity problem arising due...

Asian options are securities with a payoff that depends on the average of the underlying stock price over a certain time interval. We identify three natural assets that appear in pricing of the Asian options, namely a stock S, a zero coupon bond BT with maturity T, and an abstract asset A (an...

A callable leveraged constant maturity swap (CMS) spread note allows the holder to benefit from future changes in the spread between two swap interest rates. The issues retains the right to call the note at pre-specified times in the future. The note is priced via Monte Carlo simulation using...

In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of...