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...

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...

Risk premia are related to price probability ratios or for continuous time pure jump processes the ratios of jump arrival rates under the pricing and physical measures. The variance gamma model is employed to synthesize densities with risk premia seen as the ratio of the three parameters. The...

Portfolios are designed to maximize a conservative market value or bid price for the portfolio. Theoretically this bid price is modeled as reflecting a convex cone of acceptable risks supporting an arbitrage free equilibrium of a two price economy. When risk acceptability is completely defined...

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...

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...

Two price economy principles motivate measuring risk by the cost of acquiring the opposite of the centered or pure risk position at its upper price. Asymmetry in returns leads to differences in risk charges for short and long positions. Short risk charges dominate long ones when the upper tail...

A portfolio diversification index is defined as the ratio of an equivalent number of independent assets to the number of assets. The equivalence is based on either attaining the same diversification benefit or spread reduction. The diversification benefit is the difference in value of a value...

Stationary Increment Tempered Fractional Lévy Processes (TFLP) introduced by Boniece, Didier and Sabzikar (2020) are applied to financial data. They are used to model the stochastic drift rate of a mean reverting equation. The new processes are called OU processes with a TFLP drift rate....

Comonotone additivity for two price economy bid and ask prices motivates combining bid prices for call options with the ask prices for puts and the converse to construct two densities (termed lower and upper) reflected by these prices. Bilateral gamma models are fit to estimate these the lower...