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Option Pricing With V. G. Martingale Components

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Author Info

  • Frank Milne

    ()
    (Queen's University)

  • Dilip Madan

    (University of Maryland)

Abstract

European call options are priced when the uncertainty driving the stock price follows the V. G. stochastic process (Madan and Seneta 1990). The incomplete markets equilibrium change of measure is approximated and identified using the log return mean, variance, and kurtosis. An exact equilibrium interpretation is also provided, allowing inference about relative risk aversion coefficients from option prices. Relative to Black-Scholes, V. G. option values are higher, particularly so for out of the money options with long maturity on stocks with high means. low variances, and high kurtosis.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1159.pdf
File Function: First version 1991
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1159.

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Length: 17 pages
Date of creation: Oct 1991
Date of revision:
Publication status: Published in Mathematical Finance, Vol. 1, No. 4 (October 1991), 39-55
Handle: RePEc:qed:wpaper:1159

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Keywords: Option; pricing; Variance Gamma; martingale;

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References

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  1. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
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  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  4. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
  5. Johnson, H. E., 1983. "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 141-148, March.
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  7. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
  8. Jones, E. Philip, 1984. "Option arbitrage and strategy with large price changes," Journal of Financial Economics, Elsevier, vol. 13(1), pages 91-113, March.
  9. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317.
  10. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
  11. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
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  14. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
  15. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  16. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  17. Frank Milne & Dilip Madan & Hersh Shefrin, 1990. "The Multinomial Option Pricing Model and Its Brownian and Poisson Limits," Working Papers 1162, Queen's University, Department of Economics.
  18. 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.
  19. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(03), pages 461-474, September.
  20. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-24, July.
  21. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
  22. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
  23. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421.
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