Our goal here is to present various examples of situations where a “large” investor (i.e. an investor whose “size” challenges the liquidity or the depth of the market) sees his long-term guesses on some important financial parameters instantaneously confirmed by the market dynamics as a consequence of his trading strategy, itself based upon his guesses. These examples are worked out in the context of a model (i.e. a quantitative framework) which attempts to provide a rigorous basis for the qualitative intuitions of many practitioners. Our results may be viewed as some kind of reverse Black–Scholes paradigm where modifications of option prices affect today's real volatility.
Cite this article
P.-L. Lions, J.-M. Lasry, Instantaneous self-fulfilling of long-term prophecies on the probabilistic distribution of financial asset values. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 3, pp. 361–368DOI 10.1016/J.ANIHPC.2005.12.005