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


  • Dilip B. Madan
  • Frank Milne


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.

Suggested Citation

  • Dilip B. Madan & Frank Milne, 1992. "Contingent Claims Valued and Hedged by Pricing and Investment in a Basis," Working Papers 868, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:868

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    References listed on IDEAS

    1. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
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    Cited by:

    1. David Backus & Silverio Foresi & Liuren Wu, 2002. "Accouting for Biases in Black-Scholes," Finance 0207008, EconWPA.
    2. Joe Akira Yoshino, 2003. "Market Risk and Volatility in the Brazilian Stock Market," Journal of Applied Economics, Universidad del CEMA, vol. 6, pages 385-403, November.
    3. Mc Manus, Des, 1999. "The Information Content of Interest Rate Futures Options," Staff Working Papers 99-15, Bank of Canada.
    4. 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.).
    5. Robert R Bliss & Nikolaos Panigirtzoglou, 2000. "Testing the stability of implied probability density functions," Bank of England working papers 114, Bank of England.
    6. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics.
    7. Marie Briere, 2006. "Market Reactions to Central Bank Communication Policies :Reading Interest Rate Options Smiles," Working Papers CEB 38, ULB -- Universite Libre de Bruxelles.
    8. Grace Kuan, 2000. "Recovering Local Volatility Functions Of Forward Libor Rates," Computing in Economics and Finance 2000 255, Society for Computational Economics.

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