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Ethics in Quantitative Finance pp 221–244Cite as

Palgrave Macmillan

The Fundamental Theorem of Asset Pricing

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Abstract

The evolution of derivative markets in the twentieth century is summarised. In the aftermath of the collapse of the Bretton–Woods system in 1972, financial markets became more uncertain and, as a result, derivatives reappeared. Black and Scholes and Merton deduced an explicit equation for options prices that apparently removed uncertainty from their prices.

The Fundamental Theorem of Asset Pricing (FTAP) emerged. The significance of the FTAP is analysed, focusing on the implications of Kolmogorov’s formulation of probability.

The financial crises associated with Black Monday, in 1987, the failure of Long-Term Capital Management in 1998, The Equitable Life Assurance Company in 2002 and the Credit Crisis of 2007–2009 are described. The chapter finishes by recalling the criticisms that mathematics came in for following these crises.

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References

  • Appadurai, A. 2011. “The Ghost in the Financial Machine.” Public Culture 23 (3): 517–539.

    Google Scholar 

  • Arrow, K. J. 1964. “The Role of Securities in the Optimal Allocation of Risk-Bearing.” The Review of Economic Studies 31 (2): 91–96.

    Google Scholar 

  • Artzner, P., F. Delbaen, J. M. Eber, and D. Heath. 1999. “Coherent Measures of Risk.” Mathematical Finance 9: 203–228.

    Google Scholar 

  • Attard, B. 2000. “Making a Market. The Jobbers of the London Stock Exchange, 1800–1986.” Financial History Review 7: 5–24.

    Google Scholar 

  • Bernstein, P. L. 1998. Against the Gods, The Remarkable Story of Risk. Wiley.

    Google Scholar 

  • Beunza, D., and D. Stark. 2012. “From Dissonance to Resonance: Cognitive Interdependence in Quantitative Finance.” Economy and Society 41 (3): 383–417.

    Google Scholar 

  • Boness, A. J. 1964. “Elements of a Theory of Stock-Option Value.” The Journal of Political Economy 163–175.

    Google Scholar 

  • Brady, N. F., and others. 1988. Report of the Presidential Task Force on Market Mechanisms. U. S. Government Printing Office.

    Google Scholar 

  • Brenner, R., and G. A. Brenner. 1990. Gambling and Speculation: A Theory, a History and a Future of Some Human Decisions. Cambridge University Press.

    Google Scholar 

  • Cookson, C. 2009. “Count us in, Maths Experts Tell UK Regulator.” Financial Times, 10 June. Accessed November 2016. https://www.ft.com/content/f29248c6-554a-11de-b5d4-00144feabdc0.

  • Cox, J. C., S. A. Ross, and M. Rubinstein. 1979. “Option Pricing: A Simplified Approach.” Journal of Financial Economics 7: 229–263.

    Google Scholar 

  • Danielsson, J., P. Embrechts, C. Goodhart, C. Keating, F. Muennich, O. Renault, and H. S. Shin. 2001. An Academic Response to Basel II. Technical Report, Financial Markets Group, London School of Economics, Bank for International Settlements. www.bis.org/bcbs/ca/fmg.pdf.

  • Dowd, K., J. Cotter, C. Humphrey, and M. Woods. 2011. “How Unlucky is 25-Sigma?” arXiv:1103.5672.

    Google Scholar 

  • Edmonds, T. 2011. “Equitable Life: Penrose and Beyond.” 3 February. Accessed October 2016. http://researchbriefings.files.parliament.uk/documents/SN02953/SN02953.pdf.

  • Estrada, E., E. Uriarte, A. Montero, A. Teijeira, L. Santana, and E. De Clercq. 2000. “A Novel Approach for the Virtual Screening and Rational Design of Anticancer Compounds.” Journal of Medicinal Chemistry 43 (10): 1975–1985.

    Google Scholar 

  • Friedman, M. 1953. “The Methodology of Positive Economics.” In Essays In Positive Economics, edited by M. Friedman, 3–43. University of Chicago Press.

    Google Scholar 

  • Gordy, M. B. 2003. “A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules.” Journal of Financial Intermediation 12 (3): 199–232.

    Google Scholar 

  • Harris, M. 2015. Mathematics without Apologies: Portrait of a Problematic Vocation. Princeton University Press.

    Google Scholar 

  • Harrison, J. M., and D. M. Kreps. 1979. “Martingales and Arbitrage in Multiperiod Securities Markets.” Journal of Economic Theory 20: 381–401.

    Google Scholar 

  • Harrison, J. M., and S. R. Pliska. 1981. “Martingales and Stochastic Integrals in the Theory of Continuous Trading.” Stochastic Processes and their Applications 11: 215–260.

    Google Scholar 

  • Harrison, J. M., and S. R. Pliska. 1983. “A Stochastic Calculus Model of Continuous Trading: Complete Markets.” Stochastic Processes and their Applications 15: 313–316.

    Google Scholar 

  • Haug, E. G., and N. N. Taleb. 2011. “Option Traders use (Very) Sophisticated Heuristics, Never the Black–Scholes–Merton Formula.” Journal of Economic Behavior & Organization 77 (2): 97–106.

    Google Scholar 

  • Håvelmo, T. 1989. “The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.” 7 December. Accessed October 2016. http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1989/haavelmo-lecture.html.

  • Hull, J., and A. White. 1987. “The Pricing of Options on Assets with Stochastic Volatilities.” The Journal of Finance 42 (2): 281–300.

    Google Scholar 

  • Jaynes, E. T. 2003. Probability Theory: The Logic of Science. Cambridge University Press.

    Google Scholar 

  • Johnson, T. C. 2011. “What is Financial Mathematics?” In The Best Writing on Mathematics: 2010, edited by M. Pitic, 43–46. Princeton University Press.

    Google Scholar 

  • Kallsen, J., and A. Papapantoleon. 2016. Advanced Modelling in Mathematical Finance: In Honour of Ernst Eberlein. Springer.

    Google Scholar 

  • Kendall, M. G. 1949. “On the Reconciliation of Theories of Probability.” Biometrika 36 (1/2): 101–116.

    Google Scholar 

  • Larsen, P. T. 2007. “Goldman Pays the Price of Being Big.” Financial Times, 14 August.

    Google Scholar 

  • Levy, J. 2012. Freaks of Fortune: The Emerging World of Capitalism and Risk in America. Harvard University Press.

    Google Scholar 

  • MacKenzie, D. 2003. “Long-Term Capital Management and the Sociology of Arbitrage.” Economy and Society 32 (3): 349–380.

    Google Scholar 

  • MacKenzie, D. 2008. An Engine, Not a Camera: How Financial Models Shape Markets. The MIT Press.

    Google Scholar 

  • MacKenzie, D. 2011. “The Credit Crisis as a Problem in the Sociology of Knowledge.” American Journal of Sociology 116 (6): 1778–1841.

    Google Scholar 

  • Mandelbrot, B., and R. L. Hudson. 2005. The (Mis)Behaviour of Markets. Profile.

    Google Scholar 

  • McCloskey, D. N. 2002. The Secret Sins of Economics. Prickly Paradigm Press.

    Google Scholar 

  • McKean, H. P. 1965. “Appendix: A Free Boundary Problem for the Heat Equation Arising from a Problem in Mathematical Economics.” Industrial Management Review 6 (2): 32–39.

    Google Scholar 

  • Minoiu, C., and S. Sharma. 2014. “Financial Networks Key to Understanding Systemic Risk.” IMF Research Review, 28 May. Accessed November 2016. https://www.imf.org/external/pubs/ft/survey/so/2014/RES052314A.htm.

  • Miyazaki, H. 2007. “Between Arbitrage and Speculation: An Economy of Belief and Doubt.” History of Political Economy 36 (3): 369–415.

    Google Scholar 

  • Nelson, S. A. 1904. The ABC of Options and Arbitrage. Accessed October 2016. www.archive.org/details/abcofoptionsarbi00nelsuoft.

  • Norberg, R. 1992. “Hattendorff’s Theorem and Thiele’s Differential Equation Generalized.” Scandinavian Actuarial Journal (1): 2–14.

    Google Scholar 

  • Penrose, G. W. 2004. Report of the Equitable Life Enquiry. H. M. Stationary Office.

    Google Scholar 

  • Poincaré, H. 2001a. “Science and Hypothesis.” In The Value of Science: Essential Writings of Henri Poincaré, edited by S. J. Gould. Modern Library.

    Google Scholar 

  • Poincaré, H. 2001b. “The Value of Science.” In The Value of Science: Essential Writings of Henri Poincaré, edited by S. J. Gould. Modern Library.

    Google Scholar 

  • Reder, M. W. 2009. “Appraisal of Evidence in Economic Methodology.” In The Methodology of Positive Economics: Reflections on the Milton Friedman Legacy, edited by U. Mäki, 165–188. Cambridge University Press.

    Google Scholar 

  • Samuelson, P. A. 1965a. Foundations of Economic Analysis. Harvard University Press.

    Google Scholar 

  • Samuelson, P. A. 1965b. “Rational Theory of Warrant Pricing.” Industrial Management Review 6 (2): 13–32.

    Google Scholar 

  • Samuelson, P. A., and R. C. Merton. 1969. “A Complete Model of Warrant Pricing that Maximizes Utility.” IMR; Industrial Management Review (pre-1986) 10 (2).

    Google Scholar 

  • Shafer, G., and V. Vovk. 2006. “The Sources of Kolmogorov’s Grundbegriffe.” Statistical Science 21 (1): 70–98.

    Google Scholar 

  • Sprenkle, C. M. 1961. “Warrant Prices as Indicators of Expectations and Preferences.” Yale Economic Essays 1 (2): 178–231.

    Google Scholar 

  • Swan, E. J. 1999. Building the Global Market: A 4000 Year History of Derivatives. Kluwer Law.

    Google Scholar 

  • Sztompka, P. 2003. “Robert K. Merton.” In The {Blackwell} Companion to Major Contemporary Social Theorists, edited by G. Ritzer, 12–237. Blackwell.

    Google Scholar 

  • Tait, W. W. 1986. “Truth and Proof: The Platonism of Mathematics.” Synthese 69 (3): 341–370.

    Google Scholar 

  • Tett, G. 2009. Fools’ Gold: How Unrestrained Greed Corrupted a Dream, Shattered Global Markets and Unleashed a Catastrophe. Little Brown.

    Google Scholar 

  • Thorp, E. O. 1961. “A Favorable Strategy for Twenty-One.” Proceedings of the National Academy of Sciences 47 (1): 110–112.

    Google Scholar 

  • Thorp, E. O. 1966. Beat the Dealer: A Winning Strategy for the Game of Twenty-One. Vintage Books.

    Google Scholar 

  • Thorp, E. O. 1998. “The Invention of the First Wearable Computer.” Second International Symposium on Wearable Computers. Pittsburg: IEEE. 4–8. doi:10.1109/ISWC.1998.729523.

  • Thorp, E. O., and S. Kassouf. 1967. Beat the Market: A Scientific Stock Market System. Random House.

    Google Scholar 

  • Turner, A. 2009. “The Turner Review: A Regulatory Response to the Global Banking Crisis.” Tech. rep., Financial Services Authority.

    Google Scholar 

  • von Mises, R. 1982. Probability, Statistics and Truth. Dover.

    Google Scholar 

  • Wade Hands, D. 2009. “Did Milton Friedman’s Positive Methodology License the Formalist Revolution?” In The Methodology of Positive Economics: Reflections on the Milton Friedman Legacy, by U. Mäki, 143–164. Cambridge University Press.

    Google Scholar 

  • Zimmermann, H., and W. Hafner. 2006. “Vincenz Bronzin’s Option Pricing Theory: Contents Contribution and Background .” In Pioneers of Financial Economics: Contributions Prior to {Irving} {Fisher}, edited by G. Poitras, 169–190. Edward Elgar.

    Google Scholar 

  • Zimmermann, H., and W. Hafner. 2007. “Amazing Discovery: Vincenz Bronzin’s Option Pricing Models.” Journal of Banking and Finance 31: 531–546.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, UK

    Timothy Johnson

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Johnson, T. (2017). The Fundamental Theorem of Asset Pricing. In: Ethics in Quantitative Finance. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-61039-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-61039-9_11

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  • Print ISBN: 978-3-319-61038-2

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