Multi-factor interest-rate models are widely used. Contingent claims with early exercise features are often valued by resorting to trees, finite-difference schemes and Monte Carlo simulations. When jumps are present, however, these methods are less effective. In this work we develop an algorithm...

Energy commodities, such as oil, gas and electricity, lack the liquidity of equity markets, have large costs associated with storage, exhibit high volatilities and can have significant spikes in prices. Furthermore, and possibly most importantly, commodities tend to revert to long run...

Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent in the classical Black-Scholes-Merton model. Unfortunately, the resulting pricing problem requires solving a more difficult partial-integro differential equation (PIDE) and although several...

Diverse finite-difference schemes for solving pricing problems with Levy underliers have been used in the literature. Invariably, the integral and diffusive terms are treated asymmetrically, large jumps are truncated, the methods are difficult to extend to higher dimensions and cannot easily...

It is well known that stochastic volatility is an essential feature of commodity spot prices. By using methods of singular perturbation theory, we obtain approximate but explicit closed-form pricing equations for forward contracts and options on single- and two-name forward prices. The expansion...

Algorithmic trading (AT) and high-frequency (HF) trading, which are responsible for over 70% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this article, we employ a hidden Markov model to examine how the intraday dynamics of the...