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

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  • Franke, Günter
  • Huang, James
  • Stapleton, Richard C.

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.

Suggested Citation

  • Franke, Günter & Huang, James & Stapleton, Richard C., 2007. "Two-dimensional risk neutral valuation relationships for the pricing of options," CoFE Discussion Papers 07/08, University of Konstanz, Center of Finance and Econometrics (CoFE).
    • Handle: RePEc:zbw:cofedp:0708
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    References listed on IDEAS

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    1. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    2. repec:bla:jfinan:v:58:y:2003:i:2:p:805-820 is not listed on IDEAS
    3. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    4. Peter Ryan, 2000. "Tighter Option Bounds from Multiple Exercise Prices," Review of Derivatives Research, Springer, vol. 4(2), pages 155-188, May.
    5. 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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    Cited by:

    1. Bertram Düring, 2009. "Asset pricing under information with stochastic volatility," Review of Derivatives Research, Springer, vol. 12(2), pages 141-167, July.
    2. Marroquı´n-Martı´nez, Naroa & Moreno, Manuel, 2013. "Optimizing bounds on security prices in incomplete markets. Does stochastic volatility specification matter?," European Journal of Operational Research, Elsevier, vol. 225(3), pages 429-442.

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