Contingent Claims Valued And Hedged By Pricing And Investing In A Basis
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.
|Date of creation:||Jul 1994|
|Date of revision:|
|Publication status:||Published in Mathematical Finance, Vol. 4, No. 3 (July 1994), 223-245|
|Contact details of provider:|| Postal: |
Phone: (613) 533-2250
Fax: (613) 533-6668
Web page: http://qed.econ.queensu.ca/
More information through EDIRC
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.:
- 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.
- David C. Nachman, 1988. "Spanning and Completeness with Options," Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 311-328.
- 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.
- Robert A. Jarrow & Dilip B. Madan, 1991. "A Characterization of Complete Security Markets On A Brownian Filtration," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 31-43.
- Peter Lakner, 1993. "Martingale Measures For A Class of Right-Continuous Processes," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 43-53.
- Jarrow, Robert A., 1986. "A characterization theorem for unique risk neutral probability measures," Economics Letters, Elsevier, vol. 22(1), pages 61-65.
- Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
- Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- 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.
- 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.
- 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.
- Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130.
- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
- 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.
- Banz, Rolf W & Miller, Merton H, 1978. "Prices for State-contingent Claims: Some Estimates and Applications," The Journal of Business, University of Chicago Press, vol. 51(4), pages 653-72, October.
When requesting a correction, please mention this item's handle: RePEc:qed:wpaper:1158. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark Babcock)
If references are entirely missing, you can add them using this form.