Dynamic contributions to trading are evaluated using covariations between position and price changes a horizon. Other performance measures like Sharpe ratios, Gain loss ratios, Acceptability indices and Drawdowns are also employed. Machine learning strategies based on Gaussian Process Regression...

Complex insurance risks typically have multiple exposures. Options on multiple underliers with a short maturity are employed to hedge this exposure. Hedges are illustrated for GMWBVA accounts invested in the nine sector ETF's of the US economy. The underliers are simulated risk neutrally by...

Joint densities for a sequential pair of returns with weak autocorrelation and strong correlation in squared returns are formulated. The marginal return densities are either variance gamma or bilateral gamma. Two dimensional matching of empirical characteristic functions to its theoretical...

Multivariate return distributions consistent with bilateral gamma marginals are formulated and termed multivariate bilateral gamma (MBG). Tail probability distances and Wasserstein Distances between return data, model simulations and their squares evaluate model performance. A full Gaussian...

Financial returns at unit time are modeled as non-Gaussian limit laws. They may reflect random walks or additive processes reflecting some predictability. Mixtures of these two constructions are formulated and estimated on one minute data. It is observed that the random walk fraction is...

Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The...

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...

Minimal discounted distorted expectations across a range of stress levels are employed to model risk acceptability in markets. Interactions between discounting and stress levels used in measure changes are accommodated by lowering discount rates for the higher stress levels. Acceptability...

We consider the problem of optimal investment in a risky asset, and in derivatives written on the price process of this asset, when the underlying asset price process is a pure jump Lévy process. The duality approach of Karatzas and Shreve is used to derive the optimal consumption and...

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...