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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)

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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://www.econ.queensu.ca/working_papers/papers/qed_wp_1159.pdf
File Format: application/pdf
File Function: First version 1991
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Publisher 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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Related research
Keywords: Option pricing Variance Gamma martingale

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

References listed on IDEAS
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.:

  1. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
    Other versions:
  3. Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," Journal of Business, University of Chicago Press, vol. 60(3), pages 401-24, July. [Downloadable!] (restricted)
  4. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January. [Downloadable!] (restricted)
  5. Parkinson, Michael, 1977. "Option Pricing: The American Put," Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  8. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 493-521. [Downloadable!] (restricted)
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  11. 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. [Downloadable!] (restricted)
  12. Jones, E. Philip, 1984. "Option arbitrage and strategy with large price changes," Journal of Financial Economics, Elsevier, vol. 13(1), pages 91-113, March. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
  14. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  15. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144. [Downloadable!] (restricted)
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  16. 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. [Downloadable!] (restricted)
  17. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Eric Ghysels & Christian Gouriéroux & Joanna Jasiak, 1995. "Market Time and Asset Price Movements Theory and Estimation," CIRANO Working Papers 95s-32, CIRANO. [Downloadable!]
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  2. Elisa Luciano & Wim Schoutens, 2006. "A Multivariate Jump-Driven Financial Asset Model," Carlo Alberto Notebooks 29, Collegio Carlo Alberto. [Downloadable!]
    Other versions:
  3. Noureddine Krichene, 2005. "Subordinated Levy Processes and Applications to Crude Oil Options," IMF Working Papers 05/174, International Monetary Fund. [Downloadable!]
  4. Dilip B. Madan, 2006. "Equilibrium asset pricing: with non-Gaussian factors and exponential utilities," Quantitative Finance, Taylor and Francis Journals, vol. 6(6), pages 455-463, December. [Downloadable!] (restricted)
  5. Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, EconWPA. [Downloadable!]
  6. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA. [Downloadable!]
    Other versions:
  7. Claudia Ribeiro & Nick Webber, 2006. "Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Lévy Processes," Applied Mathematical Finance, Taylor and Francis Journals, vol. 13(4), pages 333-352, December. [Downloadable!] (restricted)
  8. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO. [Downloadable!]
  9. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes," Econometric Society 2004 North American Winter Meetings 405, Econometric Society. [Downloadable!]
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  10. Liuren Wu, 2004. "Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns," Finance 0401001, EconWPA. [Downloadable!]
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  11. Saurabha, Rritu & Tiwari, Manvendra, 2007. "Empirical Study of the effect of including Skewness and Kurtosis in Black Scholes option pricing formula on S&P CNX Nifty index Options," MPRA Paper 6329, University Library of Munich, Germany. [Downloadable!]
  12. Noureddine Krichene, 2007. "Recent Dynamics of Crude Oil Prices," IMF Working Papers 06/299, International Monetary Fund. [Downloadable!]
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