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

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  • Guenter Franke
  • James Huang

    ()

  • Richard Stapleton

    ()

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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Bibliographic Info

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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Web page: http://www.springerlink.com/link.asp?id=102989

Related research

Keywords: Option pricing; Pricing kernel; G13;

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References

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  1. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-51.
  2. Yacine Ait-Sahalia & Andrew W. Lo, 2000. "Nonparametric Risk Management and Implied Risk Aversion," NBER Working Papers 6130, National Bureau of Economic Research, Inc.
  3. Jens Carsten Jackwerth & George M. Constantinaides & Stylianos Perrakis, 2005. "Option Pricing: Real and Risk-Neutral Distributions," CoFE Discussion Paper 05-06, Center of Finance and Econometrics, University of Konstanz.
  4. Guntar Franke & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "When are Options Overpriced? The Black-Scholes Model and Alternative Characterizations of the Pricing Kernel," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-003, New York University, Leonard N. Stern School of Business-.
  5. Benninga, Simon & Mayshar, Joram, 2000. "Heterogeneity and option pricing," Research Report 00E08, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
  6. 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.
  7. Rubinstein, Mark, 1983. " Displaced Diffusion Option Pricing," Journal of Finance, American Finance Association, vol. 38(1), pages 213-17, March.
  8. 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.
  9. 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.
  10. 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.
  11. Heston, Steven L, 1993. " Invisible Parameters in Option Prices," Journal of Finance, American Finance Association, vol. 48(3), pages 933-47, July.
  12. Peter Ryan, 2000. "Tighter Option Bounds from Multiple Exercise Prices," Review of Derivatives Research, Springer, vol. 4(2), pages 155-188, May.
  13. 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.
  14. 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.
  15. Joshua Rosenberg & Robert F. Engle, 2000. "Empirical Pricing Kernels," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-014, New York University, Leonard N. Stern School of Business-.
  16. Mark Schroder, 2004. "Risk-Neutral Parameter Shifts and Derivatives Pricing in Discrete Time," Journal of Finance, American Finance Association, vol. 59(5), pages 2375-2402, October.
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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.
  3. Nicole Branger & Antje Mahayni, 2011. "Tractable hedging with additional hedge instruments," Review of Derivatives Research, Springer, vol. 14(1), pages 85-114, April.

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