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

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  • Dilip B. Madan
  • Frank Milne

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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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_868.pdf
File Function: First version 1992
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Bibliographic Info

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

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Date of creation: Nov 1992
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Handle: RePEc:qed:wpaper:868

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

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