The following titles/abstracts have been submitted by the speakers:

Peter Carr
Forward Equations for European, Barrier, and American Options in Markovian Models
We develop boundary value problems involving partial integro differential equations (PIDE's) for various kinds of options in Markovian models. The independent variables in the PIDE are strike price and maturity date. In each case, we illustrate with the variance gamma model.

C. C. Heyde
Scaling of Returns: Some Challenges for the VG Model
Amongst the standard empirical properties of risky asset returns are (1) an autocorrelation function for the returns which dies away rapidly and is statistically insignificant beyond a few lags and also (2) autocorrelation functions of squares and absolute values of returns which die away very slowly, persisting over years, or even decades. Together these indicate that, assuming returns come from a stationary process, they are not independent, but at most short-range dependent, while various functions of the returns are long-range dependent. These scaling properties are well-known, although commonly ignored for modeling convenience. However, much more can be inferred from the scaling properties of the returns. It turns out that the empirical scaling functions are initially linear and ultimately concave, which is strongly suggestive of returns distributions with infinite low order moments or alternatively that multifractal behavior is a modeling requirement. Modifications of the variance gamma model cannot readily meet these requirements. The evidence will be presented and its significance discussed, along with a class of models which can incorporate these features.

Andrey Itkin
Pricing Options with VG Model Using FFT
We discuss various analytic and numerical methods that have been used to get option prices within a framework of VG model. We show that some popular methods, for instance, Carr-Madan's FFT method could blow up for certain values of the model parameters even for European vanilla option. Alternative methods--one originally proposed by Lewis, and Heston-wise method are considered that seem to work fine for any value of the VG parameters. Test examples are given to demonstrate efficiency of these methods. Convergency of all methods is also discussed.

Dilip Madan
Using Self-Decomposable Laws in the Construction of Local Levy Processes
Four parameter Self-Decomopsable Laws are used on scaling to synthesize the options surface. Though these scaled laws are associated with the additive Sato process we recreate them as local Levy processes with a space time dependent Levy Speed function that generalizes the local volatility model of Dupire. We show that problems with vanishing forward volatilities and skews in local volatility are effectively combated by the local Levy process.
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Eugene Seneta
The Variance Gamma Process
The symmetric VG model for independent log increments (returns). Allowing for skewness of distribution, strict stationarity and long-range dependence of returns, resulting from market activity time. Volatility. The (skewed) VG and t-distributions for returns, as special cases arising from the GIG distribution for increments of market activity time. Estimation and goodness of fit in these cases. A comparison of the (symmetric) VG and scaled t-distributions.