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Two-dimensional risk neutral valuation relationships for the pricing of options

Günter Franke, James Huang and Richard C. Stapleton

No 07/08, CoFE Discussion Papers from University of Konstanz, Center of Finance and Econometrics (CoFE)

Abstract: The Black-Scholesmodelis basedona one-parameter pricingkernel with constantelasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel withat leasttwo parameters.We price European-style optionson assets whose probability distributions have two unknown parameters. We assume a pricing kernel which also has two unknown parameters. When certain conditions are met,atwo-dimensional risk-neutral valuation relationship exists for the pricing of these options: i.e. the relationshipbetween the price of the option and the prices of the underlying asset and one other option on the assetisthe sameasitwouldbe under risk neutrality.In this classofmodels,the priceof the underlying asset and that of one other option take the place of the unknown parameters.

Date: 2007
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