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Contingent Claims Valued And Hedged By Pricing And Investing In A Basis

Author

Listed:
  • Frank Milne

    () (Queen's University)

  • Dilip Madan

    (University of Maryland)

Abstract

Contingent claims with payoffs depending on finitely many asset prices are modeled as elements of 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 serves 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 are 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

  • Frank Milne & Dilip Madan, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Working Papers 1158, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1158
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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1158.pdf
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    References listed on IDEAS

    as
    1. David C. Nachman, 1988. "Spanning and Completeness with Options," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 311-328.
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    More about this item

    Keywords

    Contingent claims; options; Hilbert space; Hermite; S & P 500 index;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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