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In Honor of the Nobel Laureates Robert C. Merton and Myron S. Scholes: A Partial Differential Equation That Changed the World

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  • Robert A. Jarrow

Abstract

The Nobel Prize was given to Robert C. Merton and Myron S. Scholes for discovering a new method for determining the value of an option. This is known as the Black-Merton-Scholes option pricing formula. The purpose of this essay is to explain why the Black-Merton-Scholes option pricing formula is so important to the finance profession, the economics profession, the financial industry, and society at large. This is done by studying the history of the formula's development, the economic logic underlying the formula's derivation, and the formula's ramifications for the various professions.

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File URL: http://www.aeaweb.org/articles.php?doi=10.1257/jep.13.4.229
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Bibliographic Info

Article provided by American Economic Association in its journal Journal of Economic Perspectives.

Volume (Year): 13 (1999)
Issue (Month): 4 (Fall)
Pages: 229-248

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Handle: RePEc:aea:jecper:v:13:y:1999:i:4:p:229-248

Note: DOI: 10.1257/jep.13.4.229
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  1. 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.
  2. Merton, Robert C., 1997. "Applications of Option-Pricing Theory: Twenty-Five Years Later," Nobel Prize in Economics documents 1997-1, Nobel Prize Committee.
  3. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-57, August.
  4. 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.
  5. Miller, Merton H. & Scholes, Myron S., 1978. "Dividends and taxes," Journal of Financial Economics, Elsevier, vol. 6(4), pages 333-364, December.
  6. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December.
  7. Ross, Stephen A, 1976. "Options and Efficiency," The Quarterly Journal of Economics, MIT Press, vol. 90(1), pages 75-89, February.
  8. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  9. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
  10. 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.
  11. Jarrow, Robert A., 1994. "Derivative Security Markets, Market Manipulation, and Option Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(02), pages 241-261, June.
  12. Merton, Robert C, 1976. "The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns," Journal of Finance, American Finance Association, vol. 31(2), pages 333-50, May.
  13. Black, Fischer & Scholes, Myron, 1974. "The effects of dividend yield and dividend policy on common stock prices and returns," Journal of Financial Economics, Elsevier, vol. 1(1), pages 1-22, May.
  14. Richard Baldwin & Paul R. Krugman, 1986. "Persistent Trade Effects of Large Exchage Rate Shocks," NBER Working Papers 2017, National Bureau of Economic Research, Inc.
  15. Myers, Stewart C. & Majluf, Nicolás S., 1945-, 1984. "Corporate financing and investment decisions when firms have information that investors do not have," Working papers 1523-84., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  16. Robert C. Merton & Zvi Bodie, 1992. "On the Management of Financial Guarantees," Financial Management, Financial Management Association, vol. 21(4), Winter.
  17. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  18. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  19. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  20. Jarrow, Robert A. & van Deventer, Donald R., 1998. "The arbitrage-free valuation and hedging of demand deposits and credit card loans," Journal of Banking & Finance, Elsevier, vol. 22(3), pages 249-272, March.
  21. Jensen, Michael C. & Meckling, William H., 1976. "Theory of the firm: Managerial behavior, agency costs and ownership structure," Journal of Financial Economics, Elsevier, vol. 3(4), pages 305-360, October.
  22. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  23. 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.
  24. Myers, Stewart C. & Majluf, Nicholas S., 1984. "Corporate financing and investment decisions when firms have information that investors do not have," Journal of Financial Economics, Elsevier, vol. 13(2), pages 187-221, June.
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Cited by:
  1. Jarrow, Robert & Protter, Philip, 2005. "Large traders, hidden arbitrage, and complete markets," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2803-2820, November.
  2. Hertzler, Greg, 2000. "The Precautionary Principle in Practice: How to Write a Call Option on the Environment," 2000 Conference (44th), January 23-25, 2000, Sydney, Australia 123660, Australian Agricultural and Resource Economics Society.

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