Incomplete Markets

  • Elie Ayache


The first marvel that the market came up with against probability is the trading of the underlying asset itself. The exchange is an extraordinary matter, which is not yet fully investigated according to us. It is not that something is random (a lottery) and then we seek its value and its price. The price is there already and it cannot be anything but random because it changes. It changes because there is the minimum assumption in the market that a transaction will be followed by the next (there is, thus, the assumption of time) and that, at the next step, either the buyer or the seller is not satisfied (while his counterparty is) and will be prepared to drag the price either up or down. There is no time to try and guess or predict the next price movement in the market, because it is the exchange and trading that we are talking about and any future predictable price will trade as of now (EMH). The exchange, left to its own forces and own logic, seems thus to overturn the relation of antecedence between action and prediction.


Brownian Motion Option Price Stochastic Volatility Price Process Underlying Process 
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  1. 5.
    John H. Cochrane, Asset Pricing (Princeton and Oxford: Princeton University Press, 2001).Google Scholar
  2. 9.
    See Michael Magill and Martine Quinzii, Incomplete Markets, Volume 1, Finite Horizon Economies, International Library of Critical Writings in Economics (Cheltenham: Edward Elgar Publishing Company, 2009).Google Scholar

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© Elie Ayache 2015

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  • Elie Ayache

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