We define the class of local Lévy processes. These are Lévy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded...

The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models...

Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean-reverting square root process. The model for the mean-reverting time change is then generalized to include non-Gaussian models that...

The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced markets, written by leading scientists in this field.

The Bachelier Society for Mathematical Finance, founded in 1996, held its 1st World Congress in Paris on June 28 to July 1, 2000, thus coinciding in time with the centenary of the thesis defence of Louis Bachelier. In his thesis Bachelier introduced Brownian motion as a tool for the analysis of...

Energy commodity prices have been rising at an unprecedented pace over the last five years. As oil supplies tighten and prices frequently break new highs, major oil companies have recently unveiled a flurry of multi-billion dollar deals for new projects whose target is not oil but natural gas....

During the last decade, hedge funds have become an increasingly attractive class of assets, viewed as investments offering greater returns while risk is reduced through extensive diversification. Hedge funds have indeed grown exponentially in size, number and management style. The goal of this...

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean-reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in...

The last five years have witnessed a great momentum in the research into measures of financial risk. After many years of ad-hoc and non-consistent measures, now the problem is finally well formulated and some useful and very user-friendly solutions have been proposed. These new measures of risk...