This paper proposes a novel approach to estimating the probability weighting function (PWF) of investors in the option market. We match observed option prices to the option pricing bounds under stochastic dominance rules. Using 1-month S&P 500 index option data, we find that investors could subjectively employ an inverse S-shaped probability weighting function, which increases the weights on extreme returns and asymmetrically assigns greater weights to extremely low returns than to extremely high returns. Our findings suggest that the inverse S-shaped nature of the PWFs is robust across various estimation specifications, such as adopting an alternative methodology to construct the return distribution, and employing option data with different times to maturity.

In this paper, we propose a new spot-futures hedging method that determines the optimal hedge ratio by minimizing the riskiness of hedged portfolio returns, where the riskiness is measured by the index of Aumann and Serrano (2008). Unlike the risk measurements widely used in the literature, the riskiness index employed in our method satisfies monotonicity with respect to stochastic dominance. We also provide an empirical example to demonstrate how to estimate and test this optimal hedge ratio in equity data by the method-of-moments.

This paper proposes a new performance index referred to as the Nth-order Omega that includes the well-known Omega as a special case. The index is established by adopting an approach that is free of a utility functional form or/and distributional assumptions. A decision-theoretic foundation for our index is further established through introducing a new distribution ranking criterion. The index is monotonic with respect to Nth-degree stochastic dominance and offers a complete ordering on gambles. An empirical example of deriving the optimal hedge ratio is demonstrated to show the applicability of the index.

Marginal Conditional Stochastic Dominance (MCSD) developed by Shalit and Yitzhaki (1994) gives the conditions under which all risk-averse individuals prefer to increase the share of one risky asset over another in a given portfolio. In this paper, we extend this concept to provide conditions under which most (and not all) risk-averse investors behave in this way. Instead of stochastic dominance rules, almost stochastic dominance is used to assess the superiority of one asset over another in a given portfolio. Switching from MCSD to Almost MCSD (AMCSD) helps to reconcile common practices in asset allocation and the decision rules supporting stochastic dominance relations. A financial application is further provided to demonstrate that using AMCSD can indeed improve investment efficiency.