Daily return distributions are modeled by pure jump limit laws that are selfdecomposable laws. The returns may be seen as composed of a sum of independent and identically distributed increments or as a selfsimilar law scaling the sum of exponentially weighted past shocks or a combination...

Market clichés assert that markets take escalators up and elevators down. The observation suggests differentiating models for up and down moves. Non-diffusive models allow for this and we model the move as the difference of two independent mean reverting increasing processes driven by gamma...

When the pricing kernel is U-shaped, then expected returns of claims with payout on the upside are negative for strikes beyond a threshold, determined by the slope of the U-shaped kernel in its increasing region, and have negative partial derivative with respect to strike in the increasing...

Asset returns are modeled by bilateral gamma processes with zero covariations. Covariances are then observed to be consequences of randomness in variations. Support vector machine regressions on prices are employed to model the implied randomness. The contributions of support vector machine...

Daily asset returns are modeled using self decomposable limit laws and the structure is used to estimate the density of the uncentered data. Estimates of mean returns are a byproduct of the density estimate. Estimates of mean returns via density estimation have significantly lower standard...

A time homogeneous, purely discontinuous, parsimonous Markov martingale model is proposed for the risk neutral dynamics of equity forward prices. Transition probabilities are in the variance gamma class with spot dependent parameters. Markov chain approximations give access to option prices. The...

The theory of two price markets of Cherny and Madan (2010) yields closed forms for bid and ask prices. Defining profits as the difference between the mid quote and the risk neutral expectation and capital as difference between the ask and the bid price one obtains precise expressions for these...

For underlying asset motions calibrating skewness and kurtosis beyond the volatility it becomes possible to consider these entities as responding to their observations in past data. Models with stochastic skewness and kurtosis are constructed by allowing the second, third and fourth power...

Nonlinear martingale theory is used to form lower and upper price processes straddling a martingale. The martingale return is then modeled in terms of risk charges associated with the returns on the straddling lower and upper processes. The move to physically expected returns is made via the...

Allowing for correlated squared returns across two consecutive periods, portfolio theory for two periods is developed. This correlation makes it necessary to work with non-Gaussian models. The two period conic portfolio problem is formulated and implemented. This development leads to a mean ask...