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

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Author Info
Günter Franke () (University of Konstanz)
James Huang
Richard Stapleton

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Abstract

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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Paper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 07-08.

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Length: 34 pages
Date of creation: 27 Jun 2007
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Handle: RePEc:knz:cofedp:0708

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  1. Liu, Xiaoquan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2007. "Closed-form transformations from risk-neutral to real-world distributions," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1501-1520, May. [Downloadable!] (restricted)
  2. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51. [Downloadable!] (restricted)
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  3. 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. [Downloadable!] (restricted)
  4. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January. [Downloadable!] (restricted)
  5. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June. [Downloadable!] (restricted)
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  6. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn. [Downloadable!] (restricted)
  7. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September. [Downloadable!] (restricted)
  8. Guenter Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel," CoFE Discussion Paper 99-01, Center of Finance and Econometrics, University of Konstanz. [Downloadable!]
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  9. Benninga, Simon & Mayshar, Joram, 2000. "Heterogeneity and option pricing," Research Report 00E08, University of Groningen, Research Institute SOM (Systems, Organisations and Management). [Downloadable!]
  10. Jens Carsten Jackwerth., 1996. "Recovering Risk Aversion from Option Prices and Realized Returns," Research Program in Finance Working Papers RPF-265, University of California at Berkeley. [Downloadable!]
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  11. Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July. [Downloadable!] (restricted)
  12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  13. Rubinstein, Mark, 1983. " Displaced Diffusion Option Pricing," Journal of Finance, American Finance Association, vol. 38(1), pages 213-17, March. [Downloadable!] (restricted)
  14. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March. [Downloadable!] (restricted)
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  1. Bertram Düring, 2009. "Asset pricing under information with stochastic volatility," Review of Derivatives Research, Springer, vol. 12(2), pages 141-167, July. [Downloadable!] (restricted)
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