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Factorization of European and American option prices under complete and incomplete markets

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  • Ibáñez, Alfredo

Abstract

In a standard option-pricing model, with continuous-trading and diffusion processes, this paper shows that the price of one European-style option can be factorized into two intuitive components: One robust, X0, which is priced by arbitrage, and a second, [Pi]0, which depends on a risk orthogonal to the traded securities. This result implies the following: (1) In an incomplete market, these parts represent the price of a hedging portfolio, which is unique, and a premium, which depends only on the risk premiums associated with the residual risk, respectively. (2) In a complete market, it allows factoring the contribution of the different sources of risk to the final option price. For example, in a stochastic volatility model, we can quantify the impact on the option price of volatility risk relative to market risk, [Pi]0 and X0, respectively. Hence, certain misspricings in option markets can be directly related to the premium, [Pi]0. (3) Moreover, these results extend to American securities, which have a third component - an additional early-exercise premium.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 32 (2008)
Issue (Month): 2 (February)
Pages: 311-325

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Handle: RePEc:eee:jbfina:v:32:y:2008:i:2:p:311-325

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  1. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
  2. Merton, Robert C., 1997. "Applications of Option-Pricing Theory: Twenty-Five Years Later," Nobel Prize in Economics documents 1997-1, Nobel Prize Committee.
  3. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
  4. Tomas Björk & Irina Slinko, 2006. "Towards a General Theory of Good-Deal Bounds," Review of Finance, European Finance Association, vol. 10(2), pages 221-260.
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  7. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  8. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
  9. Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-75, July.
  10. Alfredo Ibáñez, 2003. "Robust Pricing of the American Put Option: A Note on Richardson Extrapolation and the Early Exercise Premium," Management Science, INFORMS, vol. 49(9), pages 1210-1228, September.
  11. T. Clifton Green & Stephen Figlewski, 1999. "Market Risk and Model Risk for a Financial Institution Writing Options," Journal of Finance, American Finance Association, vol. 54(4), pages 1465-1499, 08.
  12. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
  13. Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
  14. Alfredo Ibañez, 2005. "Option-Pricing in Incomplete Markets: The Hedging Portfolio plus a Risk Premium-Based Recursive Approach," Business Economics Working Papers wb058121, Universidad Carlos III, Departamento de Economía de la Empresa.
  15. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  16. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-72.
  17. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
  18. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
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Cited by:
  1. Chung, San-Lin & Hung, Mao-Wei & Wang, Jr-Yan, 2010. "Tight bounds on American option prices," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 77-89, January.

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