Risk Neutral Probabilities and Option Bounds: A Geometric Approach

Abstract

In this paper we first present a geometric approach to option bounds. We show that if two risk neutral probability density functions intersect for certain number of times, then comparing the fatness of their tails we can tell which of them gives higher option prices. Thus we can derive option bounds by identifying the risk neutral probability density function which intersects all admissible ones for certain number of times. Applying this approach we tighten the first order stochastic dominance option bounds from concurrently expiring options when the maximum value of the risk neutral density are known.

DARA and DRRA Option Bounds from Concurrently Expiring Options

“…Huang (2004b) used a new method to further improve second order stochastic dominance option bounds using more than one observed prices of options and discussed the second order arbitrage opportunities in the markets of concurrently expiring options. The method was presented by Huang (2004a) to deal with option bound problems, which takes the advantage of the distinctive feature of options' payoff 1 DARA {DRRA} denotes decreasing absolute {relative} risk aversion.…”

Option Bounds and Second Order Arbitrage Opportunities

“…We use a new technique presented by Huang (2004a), which takes the advantage of the distinctive feature of options' payoff functions. We show that given the prices of the underlying stock and n concurrently expiring options, the option bounds are given by piecewise constant pricing kernels.…”