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Contingent Claims Valued and Hedged by Pricing and Investing in a Basis

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Author Info
Dilip B. Madan
Frank Milne

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Abstract

Contingent claims with payoffs depending on finitely many asset prices are modeled as a separable Hilbert space. Under fairly general conditions, including market completeness, it is shown that one may change measure to a reference measure under which asset prices are Gaussian and for which the family of Hermite polynomials serve as an orthonormal basis. Basis pricing synthesizes claim valuation and basis investment provides static hedging opportunities. For claims written as functions of a single asset price we infer from observed option prices the implicit prices of basis elements and use these to construct the implied equivalent martingale measure density with respect to the reference measure which in this case is the Black Scholes Geometric Brownian motion model. Data on S&P 500 options from the Wall Street Journal is used to illustrate the calculations involved. On this illustrative data set the equivalent martingale measure deviates from the Black-Scholes model by relatively discounting the larger price movements with a compensating premia placed on the smaller movements.

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Publisher Info
Paper provided by Queen's University, Department of Economics in its series Working Papers with number 868.

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Length: 38 pages
Date of creation: 1992
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Handle: RePEc:qed:wpaper:868

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Keywords: investments ; pricing;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Back, Kerry & Pliska, Stanley R., 1991. "On the fundamental theorem of asset pricing with an infinite state space," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 1-18. [Downloadable!] (restricted)
  2. Amershi, Amin H, 1985. " A Complete Analysis of Full Pareto Efficiency in Financial Markets for Arbitrary Preferences," Journal of Finance, American Finance Association, vol. 40(4), pages 1235-43, September. [Downloadable!] (restricted)
  3. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  4. David C. Nachman, 1988. "Spanning and Completeness with Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 1(3), pages 311-328. [Downloadable!] (restricted)
  5. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February. [Downloadable!] (restricted)
  6. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 573-92. [Downloadable!] (restricted)
  7. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October. [Downloadable!] (restricted)
  8. John, Kose, 1984. "Market Resolution and Valuation in Incomplete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(01), pages 29-44, March. [Downloadable!]
  9. Jarrow, Robert A., 1986. "A characterization theorem for unique risk neutral probability measures," Economics Letters, Elsevier, vol. 22(1), pages 61-65. [Downloadable!] (restricted)
  10. John, Kose, 1981. "Efficient Funds in a Financial Market with Options: A New Irrelevance Proposition," Journal of Finance, American Finance Association, vol. 36(3), pages 685-95, June. [Downloadable!] (restricted)
  11. Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," Journal of Business, University of Chicago Press, vol. 51(4), pages 653-72, October. [Downloadable!] (restricted)
  12. Green, Richard C. & Jarrow, Robert A., 1987. "Spanning and completeness in markets with contingent claims," Journal of Economic Theory, Elsevier, vol. 41(1), pages 202-210, February. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Paolo Guasoni, 2004. "Estimating state price densities by Hermite polynomials: theory and application to the Italian derivatives market," Temi di discussione (Economic working papers) 507, Bank of Italy, Economic Research Department. [Downloadable!]
  2. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA. [Downloadable!]
  3. Joe Akira Yoshino, 2003. "Market Risk and Volatility in the Brazilian Stock Market," Journal of Applied Economics, Universidad del CEMA, vol. 0, pages 385-403, November. [Downloadable!]
  4. Grace Kuan, 2000. "Recovering Local Volatility Functions Of Forward Libor Rates," Computing in Economics and Finance 2000 255, Society for Computational Economics. [Downloadable!]
  5. Bertholon, H. & Monfort, A. & Pegoraro, F., 2007. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Documents de Travail 188, Banque de France. [Downloadable!]
    Other versions:
  6. Christian Gourieroux & Joann Jasiak, 2001. "Dynamic Factor Models," Econometric Reviews, Taylor and Francis Journals, vol. 20(4), pages 385-424. [Downloadable!] (restricted)
  7. Steven A. Weinberg, 2001. "Interpreting the volatility smile: an examination of the information content of option prices," International Finance Discussion Papers 706, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
  8. Robert R Bliss & Nikolaos Panigirtzoglou, . "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England. [Downloadable!]
  9. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics. [Downloadable!]
  10. Jondeau, E. & Rockinger, M., 1998. "Reading the Smile: The Message Conveyed by Methods Which Infer Risk Neutral," Documents de Travail 47, Banque de France. [Downloadable!]
  11. Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Working Papers 99-15, Bank of Canada. [Downloadable!]
  12. Marie Brière, 2006. "Market Reactions to Central Bank Communication Policies : Reading Interest Rate Options Smiles," Working Papers CEB 06-009.RS, Université Libre de Bruxelles, Solvay Brussels School of Economics and Management, Centre Emile Bernheim (CEB). [Downloadable!]
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