Two-Dimensional Risk-Neutral Valuation Relationships for the Pricing of Options

Abstract

We generalize the concept of a risk-neutral valuation relationship in order to price options in cases where the restrictive conditions required for a traditional one-dimensional risk-neutral valuation relationship do not apply. We derive conditions under which a two-dimensional risk-neutral valuation relationship exists, relating the price of an option on an asset to the prices of the underlying asset and one other option on the asset. This allows us to price contingent claims in economies where the pricing kernel exhibits non-constant elasticity.