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Future Possibilities in Finance Theory and Finance Practice

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Mathematical Finance — Bachelier Congress 2000

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Abstract

The origins of much of the mathematics in modern finance can be traced to Louis Bachelier’s 1900 dissertation on the theory of speculation, framed as an option-pricing problem. This work marks the twin births of both the continuous-time mathematics of stochastic processes and the continuous-time economics of derivative-security pricing. In solving his option-pricing problem, Bachelier provides two different derivations of the classic partial differential equation for the probability density of what later was called a Wiener process or Brownian motion process. In one derivation, he writes down a version of what is now commonly called the Chapman—Kolmogorov convolution probability integral in one of the earliest examples of that integral in print. In the other, he uses a limit argument applied to a discrete-time binomial process to derive the continuous-time transition probabilities. Bachelier also develops the method of images (or reflection) to solve for a probability function of a diffusion process with an absorbing barrier. All this in his thesis five years before the publication of Einstein’s mathematical theory of Brownian motion.

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References

  • Arrow, K.J. (1953), “Le Rôle des Valeurs Boursières pour la Répartition la Meilleure des Risques,” Econometrie, Colloques Internationaux du Centre National de la Recherche Scientifique, Vol. XI, Paris, 41–7.

    Google Scholar 

  • Bachelier, L. (1900), “Théorie de la Spéculation,” Annales de l’Ecole Normale Supérieure, 3, Paris: Gauthier-Villars. English translation in Cootner, P.H. (1964).

    Google Scholar 

  • Banz, R.W., M.H. Miller (1978), “Prices for State-Contingent Claims: Some Estimates and Applications,” Journal of Business, 51 (October): 653–72.

    Article  Google Scholar 

  • Bernstein, P.L. (1992), Capital Ideas: The Improbable Origins of Modem Wall

    Google Scholar 

  • Street, New York: Free Press. Black, F. (1989), “How We Came Up With the Option Formula,” Journal of Portfolio Management, 15 (Winter): 4–8.

    Google Scholar 

  • Black F., M. Scholes (1973), “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, 81 (May-June): 637–54.

    Article  Google Scholar 

  • Bodie, Z. (1995), “On the Risk of Stocks in the Long Run,” Financial Analysts Journal, (May-June): 18–22.

    Google Scholar 

  • Bodie, Z. (1996), “What the Pension Benefit Guaranty Corporation Can Learn from the Federal Savings-and-Loan Insurance Corporation,” Journal of Financial Services Research, 10 (January): 83–100. Bodie, Z. (2000), “Financial Engineering and Social Security Reform,” in Risk Aspects of Investment-Based Social Security Reform, eds. J. Campbell, M. Feldstein, Chicago: University of Chicago Press.

    Google Scholar 

  • Bodie, Z., R.C. Merton (1993), “Pension Benefit Guarantees in the United States: A Functional Analysis,” in R. Schmitt, ed., The Future of Pensions in the United States, Pension Research Council, Philadelphia: University of Pennsylvania Press: 195–234.

    Google Scholar 

  • Bodie, Z., R.C. Merton, W. Samuelson (1992), “Labor Supply Flexibility and Portfolio Choice in a Life-Cycle Model,” Journal of Economic Dynamics and Control, 16: 427–449.

    Article  Google Scholar 

  • Breeden, D.T. (1979), “An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities,” Journal of Financial Economics, 7 (September): 265–96.

    Article  MATH  Google Scholar 

  • Breeden, D.T., R. Litzenberger (1978), “Prices of State-Contingent Claims Implicit in Option Prices,” Journal of Business, 51 (October): 621–51.

    Article  Google Scholar 

  • Claessens, S., T. Glaessner, D. Klingebiel (2000), “Electronic Finance: Reshaping the Financial Landscape Around the World,” Financial Sector Discussion Paper No. 4 (September) The World Bank.

    Google Scholar 

  • Cootner, P.H., ed. (1964), The Random Character of Stock Market Prices, Cambridge, MA: MIT Press.

    Google Scholar 

  • Cox, J.C., C. Huang (1989), “Optimum Consumption and Portfolio Policies When Asset Prices Follow a Diffusion Process,” Journal of Economic Theory, 49 (October): 33–83.

    Article  MathSciNet  MATH  Google Scholar 

  • Crane, D., et al (1995), The Global Financial System: A Functional Perspective, Boston: Harvard Business School Press.

    Google Scholar 

  • Cummins, J.D. (1988), “Risk-Based Premiums for Insurance Guarantee Funds,” Journal of Finance, 43 (September): 823–89.

    Article  MathSciNet  Google Scholar 

  • Cummins, J.D., H. Geman (1995), “Pricing Catastrophe Insurance Futures and Call Spreads: An Arbitrage Approach,” Journal of Fixed Income, ( March ): 46–57.

    Google Scholar 

  • Friedman, B.M. (2000), “Decoupling at the Margin: The Threat to Monetary Policy from the Electronic Revolution in Banking,” National Bureau of Economic Research Working Paper No. W7955, Cambridge, MA: October.

    Google Scholar 

  • Hakansson, N.H. (1976), “The Purchasing Power Fund: A New Kind of Financial Intermediary,” Financial Analysts Journal, 32 (November-December): 49–59.

    Article  Google Scholar 

  • Harrington, S., S. Mann, G. Niehaus (1995), “Insurer Capital Structure Decisions and the Viability of Insurance Derivatives,” Journal of Risk and Insurance, 62 ( September): 483–508.

    Article  Google Scholar 

  • Hayes, J., J. Cole, D. Meiselman (1993), “Health Insurance Derivatives: The Newest Application of Modern Financial Risk Management,” Business Economics, 28 ( April): 36–40.

    Google Scholar 

  • ltd, K. (1951), “On Stochastic Differential Equations,” Memoirs of American Mathematical Society, 4: 1–51.

    Google Scholar 

  • ltd, K. (1987), Kiyoshi ltd Selected Papers, New York: Springer-Verlag.

    Google Scholar 

  • ltd, K., H.P. McKean, Jr. (1964), Diffusion Processes and Their Sample Paths, New York: Academic Press.

    Google Scholar 

  • Kraus, A., S.A. Ross (1982), “The Determination of Fair Profits for the Property-Liability Insurance Firm,” Journal of Finance, 37 (September): 1015–28.

    Article  Google Scholar 

  • Jin, L., L. Kogan, T. Lim, J. Taylor, A. Lo (1997), “The Derivatives Sourcebook: A Bibliography of Applications of the Black-Scholes/Merton Option-Pricing Model,” Sloan School of Management, Massachusetts Institute of Technology Working Paper. Web site: http://forbin.mit.eclu/clsp/

    Google Scholar 

  • Marcus, A.J. (1987), “Corporate Pension Policy and the Value of PBGC Insurance,” in Z. Bodie, J.B. Shoven, D.A. Wise, eds., Issues in Pension Economics, Chicago, IL: University of Chicago Press.

    Google Scholar 

  • Markowitz, H. (1952), “Portfolio Selection,” Journal of Finance, 7 (March): 77–91.

    Google Scholar 

  • Mayers, D. (1972), “Non-Marketable Assets and Capital Market Equilibrium Under Uncertainty,” in M. Jensen, ed., Studies in the Theory of Capital Markets, New York: Praeger.

    Google Scholar 

  • McKean, Jr., H.P. (1965), “Appendix: A Free Boundary Problem for the Heat Equation Arising From a Problem in Mathematical Economics,” Industrial Management Review, 6 (Spring): 32–9.

    MathSciNet  Google Scholar 

  • Melnikov, A.V. (1999), “On Innovation and Risk Aspects of Financial System Evolution,” Questions of Risk Analysis, 1,1: 22–27 (in Russian).

    Google Scholar 

  • Melnikov, A.V. (forthcoming), “Financial System: Innovations and Pricing Risks,” Journal of Korean Mathematical Society.

    Google Scholar 

  • Merton, R.C. (1969), “Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case,” Review of Economics and Statistics, 51 (August): 247–57.

    Article  Google Scholar 

  • Merton, R.C. (1970), “A Dynamic General Equilibrium Model of the Asset Market and its Application to the Pricing of the Capital Structure of the Firm,” Working Paper No$1497–70, Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA. Reprinted in Merton (1992, Ch. 11 ).

    Google Scholar 

  • Merton, R.C. (1971), “Optimum Consumption and Portfolio Rules in a Continuous-Time Model,” Journal of Economic Theory, 3 (December): 373–413.

    Article  MathSciNet  MATH  Google Scholar 

  • Merton, R.C. (1972), “Appendix: Continuous-Time Speculative Processes,” in R.H. Day,S.M. Robinson, eds., Mathematical Topics in Economic Theory and Computation, Philadelphia, PA: Society for Industrial and Applied Mathematics. Reprinted in SIAM Review, 15 (January 1973): 34–8.

    Google Scholar 

  • Merton, R.C. (1973a), “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, 4 (Spring): 141–83.

    Article  MathSciNet  Google Scholar 

  • Merton, R.C. (1973b), “An Intertemporal Capital Asset Pricing Model,” Econometrica, 41 (September): 867–87.

    Article  MathSciNet  MATH  Google Scholar 

  • Merton, R.C. (1977a), “An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees: An Application of Modern Option Pricing Theory,” Journal of Banking and Finance, 1 (June): 3–11.

    Article  Google Scholar 

  • Merton, R.C. (1977b), “A Reexamination of the Capital Asset Pricing Model,” in Studies in Risk and Return, J. Bicksler, I. Friend, eds., Cambridge, MA: Ballinger, Vol. I & II: 141–159.

    Google Scholar 

  • Merton, R.C. (1982), “On the Microeconomic Theory of Investment Under Uncertainty,” in Handbook of Mathematical Economics, Volume II, K. Arrow, M. Intriligator, eds., Amsterdam: North-Holland Publishing Company.

    Google Scholar 

  • Merton, R.C. (1983a), “On Consumption-Indexed Public Pension Plans,” in Financial Aspects of the U.S. Pension System, Z. Bodie and J. Shoven, eds., Chicago: University of Chicago Press.

    Google Scholar 

  • Merton, R.C. (1983b), “Financial Economics,” in E.G. Brown, R.M. Solow, eds., Paul Samuelson and Modern Economic Theory, New York: McGraw- Hill.

    Google Scholar 

  • Merton, R.C. (1990), “The Financial System and Economic Performance,” Journal of Financial Services Research, 4, (December): 263–300.

    Article  Google Scholar 

  • Merton, R.C. (1992), Continuous-Time Finance, Revised Edition, Cambridge, MA: Basil Blackwell.

    Google Scholar 

  • Merton, R.C. (1993a), “Operation and Regulation in Financial Intermediation: A Functional Perspective,” in P. Englund, ed., Operation and Regulation of Financial Markets, Stockholm: The Economic Council.

    Google Scholar 

  • Merton, R.C. (1993b), “Optimal Investment Strategies for University Endowment Funds,” in C. Clotfelter, M. Rothschild, eds., Studies of Supply and Demand in Higher Education, Chicago: University of Chicago Press.

    Google Scholar 

  • Merton, R.C. (1994), “Influence of Mathematical Models in Finance on Practice: Past, Present and Future,” Philosophical Transactions of the Royal Society of London, Vol. 347, (June): 451–463.

    Article  Google Scholar 

  • Merton, R.C. (1995a), “A Functional Perspective of Financial Intermediation,” Financial Management, Vol. 24, No. 2, (Summer): 23–41.

    Article  Google Scholar 

  • Merton, R.C. (1995b), “Financial Innovation and the Management and Regulation of Financial Institutions,” Journal of Banking and Finance, 19 (June): 461–481.

    Article  Google Scholar 

  • Merton, R.C. (1997), “On the Role of the Wiener Process in Finance Theory and Practice: The Case of Replicating Portfolios,” in D. Jerison, I.M. Singer, D.W. Stroock, eds., The Legacy of Norbert Wiener: A Centennial Symposium, PSPM Series, Vol. 60, Providence, RI: American Mathematical Society.

    Google Scholar 

  • Merton, R.C. (1998), “Applications of Option-Pricing Theory: Twenty-Five Years Later,” Les Prix Nobel 1997, Stockholm: Nobel Foundation; reprinted in American Economic Review, (June): 323–349.

    Google Scholar 

  • Merton, R.C. (1999), “Commentary: Finance Theory and Future Trends: The Shift to Integration,” Risk, ( July ): 48–50.

    Google Scholar 

  • Merton, R.C., Z. Bodie (1992), “On the Management of Financial Guarantees,” Financial Management, 21 (Winter): 87–109.

    Article  Google Scholar 

  • Merton, R.C., Z. Bodie (1993), “Deposit Insurance Reform: A Functional Approach,” in A. Meitzer and C. Plosser, eds., Carnegie-Rochester Conference Series on Public Policy, Vol. 38, (June): 1–34.

    Google Scholar 

  • Merton, R.C., M.S. Scholes (1995), “Fischer Black,” Journal of Finance, 50 (December): 1359–1370.

    Article  Google Scholar 

  • Merton, S.J. (1992), “Options Pricing in the Real World of Uncertainties: Educating Towards a Flexible Labor Force,” B.A. Thesis, Department of Economics, Harvard University, March 18, 1992.

    Google Scholar 

  • Meulbroek, L.K. (2000), “Total Strategies for Company-Wide Risk Control,” Financial Times, 9 May, Mastering Risk series: 1–4.

    Google Scholar 

  • Mody, A. (1996), “Valuing and Accounting for Loan Guarantees,” World Bank Research Observer, 11, No. 1: 119–42.

    Article  Google Scholar 

  • Nasar, S. (1992), “For Fed, a New Set of Tea Leaves,” New York Times, 5 July, sec. D:l.

    Google Scholar 

  • Neal, R.S. (1996), “Credit Derivatives: New Financial Instruments for Controlling Credit Risk,” Federal Reserve Bank of Kansas City Economic Review, 81 (Second Quarter): 14–27.

    Google Scholar 

  • Ross, S. A. (1976a), “Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory, 13 (December): 341–60.

    Article  MathSciNet  Google Scholar 

  • Ross, S. A. (1976b), “Options and Efficiency,” Quarterly Journal of Economics, 90 (February): 75–89.

    Article  MATH  Google Scholar 

  • Samuelson, P.A. (1965), “Rational Theory of Warrant Pricing,” Industrial Management Review, 6 (Spring): 13–31.

    Google Scholar 

  • Samuelson, P.A. (1971), “The ‘Fallacy’ of Maximizing the Geometric Mean in Long Sequences of Investing or Gambling,” Proceedings of the National Academy of Sciences, 68: 2493–2496.

    Article  MathSciNet  MATH  Google Scholar 

  • Samuelson, P.A. (1972), “Mathematics of Speculative Price,” in R.H. Day, S.M. Robinson, eds., Mathematical Topics in Economic Theory and Computation, Philadelphia, PA: Society for Industrial and Applied Mathematics. Reprinted in SIAM Review, 15 (January 1973): 1–42.

    Google Scholar 

  • Samuelson, P.A. (1979), “Why We Should Not Make Mean Log of Wealth Big Though Years to Act Are Long,” Journal of Banking and Finance, 3: 305–307.

    Article  Google Scholar 

  • Samuelson, P.A., R.C. Merton (1969), “A Complete Model of Warrant Pricing that Maximizes Utility,” Industrial Management Review, 10 (Winter): 17–46.

    Google Scholar 

  • Scholes, M.S. (1998), “Derivatives in a Dynamic Environment,” Les Prix Nobel 1997, Stockholm: Nobel Foundation.

    Google Scholar 

  • Sharpe, W. F. (1964), “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, 19 (September): 425–42.

    Google Scholar 

  • Smetters, K. (1997), “Investing the Social Security Trust Fund in Equities: An Option Pricing Approach,” Technical Paper Series, Macroeconomic Analysis and Tax Analysis Divisions, Washington, DC.

    Google Scholar 

  • Sosin, H. (1980), “On the Valuation of Federal Loan Guarantees to Corporations,” Journal of Finance, 35 (December): 1209–21.

    Article  Google Scholar 

  • Tobin, J. (1958), “Liquidity Preference as Behavior Towards Risk,” Review of Economic Studies, 25 (February): 68–85.

    Article  Google Scholar 

  • Trigeorgis, L. (1993), “Real Options and Interactions with Financial Flexibility,” Financial Management, 22 (Autumn): 202–24.

    Article  Google Scholar 

  • Turvey, C. (1992), “Evaluating Premiums for Farm Income Insurance Policy,” Canadian Journal of Agricultural Economics, 40, No. 2: 183–98.

    Article  Google Scholar 

  • Williams, J. (1978), “Risk, Human Capital, and the Investor’s Portfolio,” Journal of Business, 51: 65–89.

    Article  Google Scholar 

  • Williams, J. (1979), “Uncertainty and the Accumulation of Human Capital Over the Life Cycle,” Journal of Business, 52: 521–48.

    Article  Google Scholar 

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Authors and Affiliations

  1. Havard Business School, Morgan Hall 397, Soldiers Field, Boston, MA, 02163, USA

    Robert C. Merton

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  1. Robert C. Merton
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Editors and Affiliations

  1. CEREMADE, UMR CNRS 7534, Université Paris IX-Dauphine, Place du Maréchal De Lattre De Tassigny, 75775, Paris Cedex 16, France

    Hélyette Geman

  2. Groupe ESSEC, Av. Bernhard-Hirsch, B.P. 50105, 95021, Cergy-Pontoise Cedex, France

    Hélyette Geman

  3. Robert H. Smith School of Business, University of Maryland, 4427 Van Munching Hall, 20742, College Park, MD, USA

    Dilip Madan

  4. Department of Finance, University of Illinois, 242 University Hall, 601 South Morgan Street, 60607-7, Chicago, IL, USA

    Stanley R. Pliska

  5. Erasmus Universiteit Rotterdam, Postbus 1738, 3000 DR, Rotterdam, The Netherlands

    Ton Vorst

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Merton, R.C. (2002). Future Possibilities in Finance Theory and Finance Practice. In: Geman, H., Madan, D., Pliska, S.R., Vorst, T. (eds) Mathematical Finance — Bachelier Congress 2000. Springer Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12429-1_3

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  • DOI: https://doi.org/10.1007/978-3-662-12429-1_3

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