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Probability and Contingency

  • Jon Roffe

Abstract

To begin with the obvious: there are many markets, and many kinds of markets. It would be easy to insist as a result that the use of the indefinite article in ‘ the market’ is nothing more than a matter of convenience, and that any attempt to elaborate a theory of the market in the singular is bound to fall into either triviality, overgeneralization, or both. Perhaps.

Keywords

Option Price Price Model Future State Implied Volatility Strike Price 
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Notes

  1. 1.
    John Downes and Jordan Goodman, Dictionary of Finance and Investment Terms, 8th edition (New York: Barron’s Educational Series, Inc., 2002), 182.Google Scholar
  2. 3.
    See, however, Alireza M. Gharagozlou, ‘Unregulable: why derivatives may never be regulated,’ Brooklyn Journal of Corporate, Financial & Commercial Law 4 (2010), 273. Gharagozlou argues that the fact that derivatives are contracts from the point of view of the law that they are unable to be adequately regulated at all. Later, we will see that there is a more significant reason yet again for thinking that market regulation, considered as a set of rules that restrict the range of formulations of pricing mechanisms, is a poorly formu lated notion.Google Scholar
  3. 4.
    Aristotle, Politics, trans. T.A. Sinclair, revised Trevor J. Saunders (London: Penguin, 1992), 90; §1259a3ff.Google Scholar
  4. 5.
    Louis Bachelier, ‘The Theory of Speculation,’ in Louis Bachelier’s theory of specu lation: the origins of modern finance, trans. Mark Davis and Alison Etheridge (Princeton, NJ: Princeton University Press, 2006), 15–79.Google Scholar
  5. 6.
    For a summary of the most important objections, see D.H. Goldenberg, ‘A unified method for pricing options on diffusion processes,’ Journal of Financial Economics 29 (1991), 3–34.CrossRefGoogle Scholar
  6. 7.
    Fischer Black and Myron Scholes, ‘The Pricing of Options and Corporate Liabilities,’ Journal of Political Economy 81 (1973), 637–54;CrossRefGoogle Scholar
  7. Robert Merton, ‘The Theory of Rational Option Pricing,’ Bell Journal of Economics and Management Science 4 (1973), 141–83. On their respective roles, see Ayache’s footnote at The Blank Swan: The End of Probability (Chichester: Wiley & Sons, 2010), 67n4. The Section (66–70) to which the notes belongs also provides a good summary presentation of the mathematics of the partial differential equation that constitutes BSM.CrossRefGoogle Scholar
  8. For a helpful comparison of Bachelier’s account of options pricing with that of BSM, see Walter Schachermayer and Josef Teichmann, ‘How Close are the Options Pricing Formulas of Bachelier and Black-Merton-Scholes?,’ Mathematical Finance 18:1 (2008), 155–70.CrossRefGoogle Scholar
  9. 8.
    See Donald Mackenzie, An Engine, Not a Camera (Cambridge, MA.: The MIT Press, 2006), 141–2.CrossRefGoogle Scholar
  10. 9.
    Nassim Taleb, The Black Swan: The Impact of the Highly Improbable (New York: Random House, 2007)Google Scholar
  11. 11.
    Nassim Taleb, Antifragile: Things that Gain from Disorder (London: Random House, 2012).Google Scholar
  12. 12.
    Immanuel Kant, Critique of Pure Reason, ed. and trans. Paul Guyer and Allen Wood (Cambridge: Cambridge University Press, 1998), A235B295.CrossRefGoogle Scholar
  13. 13.
    David Hume, A Treatise of Human Nature, ed. LA Selby-Bigge (Oxford: Clarendon Press, 1896), 69–175.Google Scholar
  14. 17.
    I note in passing that, for Ayache, Meillassoux’s engagement with this ‘neces sitarian probabilistic argument’ (BSEP 135) constitutes the weakest moment of After Finitude, insofar as it impoverishes the temporal dimension of the analysis. In a passage whose obliquity should not distract from its import (as the discussion of the temporal character of the market and of debt in chapters to come will argue), Ayache writes that ‘Meillassoux’s speculation is relieved from the depth of the past, as well as from its debt […] As to the future of the world as such, my claim is that Meillassoux is relieved from its responsibility too because of his responsibility only towards speculation and of his escape from philosophical credit’ (BSEP 151). The necessity of refounding the project of After Finitude in relation to time is treated in the final chapter below. In a related series of passages (BSEP 155ff), Ayache aligns this weakness in Meillassoux’s argument with an impoverished theory of the event, and argues that, rather than trying to derive the necessity of contingency finally from the impossibility of mathematical totalization (which he cannot achieve in absolute terms, something Meillassoux himself admits [AF 105]), a theory of the event qua form of the future is what is missing, it is ‘his missing derivation’ (BSEP 156). It is also worth pointing out that this line of critical argumentation is grounds for rejecting some of the more ridiculous suggestions about the underlying cause of the credit crisis, such as the claim advanced by the president of the rating agency Standard and Poor’s that losses of the kind experienced in the credit derivatives market are rare but predictable, and would likely take place every 763 years: ‘the implied risk-neutral probability of a catastrophic meltdown scenario is very small with an expected (risk-neutral) waiting time of about 763 years on average.’ (Francis Longstaff and Arvind Rajan, ‘An Empirical Analysis of the Pricing of Collateralized Debt Obligations,’ The Journal of Finance 63:2 [April 2008], 551.)CrossRefGoogle Scholar
  15. 18.
    Gilles Deleuze, Bergsonism, trans. Hugh Tomlinson (New York: Zone Books, 1991), 98.Google Scholar
  16. 19.
    On the notion of badly analysed composites and the Bergsonian method for addressing their role in thought, see Keith Ansell-Pearson, ‘Bergson’ in The Routledge Companion to Nineteenth Century Philosophy, ed. Dean Moyar (New York: Routledge, 2010), 419–21.Google Scholar
  17. 23.
    Elie Ayache, ‘Single-case Statistics?’ Wilmott (February 2011), 13.Google Scholar
  18. 26.
    Ayache also argues, traders themselves have no particular investment in the implicit metaphysics of probability and make use of BSM and the other forms of probabilistic inference in just this direct fashion. He is supported in this view, as it happens, by Nassim Taleb — see Emanuel Derman and Nassim Taleb, ‘The Illusions of Dynamic Replication,’ Quantitative Finance 5:4 (2005), 323–6, esp. 323.CrossRefGoogle Scholar

Copyright information

© Jon Roffe 2015

Authors and Affiliations

  • Jon Roffe
    • 1
  1. 1.University of New South WalesAustralia

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