CONTINGENT CLAIMS VALUED AND HEDGED BY PRICING AND INVESTING IN A BASIS

Frank Milne () and Dilip Madan
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Dilip Madan: University of Maryland

No 1158, Working Papers from Queen's University, Department of Economics

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.

Keywords: Contingent claims; options; Hilbert space; Hermite; S & P 500 index (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
Date: 1994-07
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Published in Mathematical Finance, Vol. 4, No. 3 (July 1994), 223-245

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http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1158.pdf First version 1994 (application/pdf)

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Journal Article: CONTINGENT CLAIMS VALUED AND HEDGED BY PRICING AND INVESTING IN A BASIS (1994)
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Persistent link: http://EconPapers.repec.org/RePEc:qed:wpaper:1158

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