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

  • Guenter Franke
  • James Huang

    ()

  • Richard Stapleton

    ()

The Black-Scholes model is based on a one-parameter pricing kernel with constant elasticity. Theoretical and empirical results suggest declining elasticity and, hence, a pricing kernel with at least two parameters. We price European-style options on assets whose probability distributions have two unknown parameters. We assume a pricing kernel which also has two unknown parameters. When certain conditions are met, a two-dimensional risk-neutral valuation relationship exists for the pricing of these options: i.e. the relationship between the price of the option and the prices of the underlying asset and one other option on the asset is the same as it would be under risk neutrality. In this class of models, the price of the underlying asset and that of one other option take the place of the unknown parameters.

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File URL: http://hdl.handle.net/10.1007/s11147-007-9009-3
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Article provided by Springer in its journal Review of Derivatives Research.

Volume (Year): 9 (2006)
Issue (Month): 3 (November)
Pages: 213-237

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Handle: RePEc:kap:revdev:v:9:y:2006:i:3:p:213-237
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  1. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
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