Acceptable Bilateral Gamma Parameters

TL;DR

This paper develops statistical methods to infer acceptance sets of risky assets modeled by bilateral gamma distributions from market prices, highlighting behavioral implications and estimating risk parameters.

Contribution

It introduces a novel approach to estimate acceptance set boundaries for bilateral gamma distributed cash flows using market data, linking to prospects theory.

Findings

Boundaries for bilateral gamma risk parameters are estimated and validated against market data.

Prospects theory naturally explains the behaviors implied by the acceptance set boundaries.

Comparison with empirical facts shows consistency with known risk measure acceptance sets.

Abstract

The purpose of this paper is to utilize statistical methodologies to infer from market prices of assets and their derivatives the magnitude of the set of a measure M that defines acceptance sets of risky future cash flows. Specifically, we estimate upper and lower boundaries of the compensation needed for a given bilateral gamma distributed future cash flow to be acceptable. We show that prospects theory provides a natural interpretation of the behaviors implied by such boundaries, which are not compatible with expected utility theory over terminal wealth. Boundaries for bilateral gamma risk neutral scale parameters for given speed parameters are also estimated and tested against market data and, in particular, comparisons are made with known empirical facts about the magnitude of the acceptance set of a common class of risk measures.