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 Levy process. The duality approach of Karatzas and Shreve is used to derive the optimal consumption and investment...

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...

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 contrast two different asset pricing models, where the pricing kernel either (i) increases in the volatility dimension, reflecting investors' aversion to volatility, or (ii) could be non-monotonic in volatility, reflecting heterogeneity in investors' beliefs. The two models yield opposite...

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...

We propose a model of volatility tail behavior, in which the pricing measure dominates the physical measure in both tails of the volatility distribution and, hence, the derived pricing kernel exhibits an increasing and decreasing region in the volatility dimension. The model features investors...

Equity market interactions with their the option markets are modeled using a two state hidden Markov model permitting transitioning between states when the asset market leads and when the option markets lead. Data on S&P 500 returns and returns on the VIX are employed to filter state...

The Sato process associated with self decomposable laws at unit time is further generalized to an additive process with arbitrary innovation term structures. A second generalization to additive processes consistent with bilateral gamma marginal distributions is also made. The Sato process is a...

This paper characterizes performance measures satisfying a set of proposed axioms. We develop four new measures consistent with the axioms and show that they improve on the economic properties of the Sharpe Ratio and the Gain-Loss Ratio. In our treatment, the performance measures, or the indices...

This study formalizes the departure between risk-neutral and physical index return volatilities, termed volatility spreads. Theoretically, the departure between risk neutral and physical index volatility is connected to the higher-order physical return moments and the parameters of the pricing...