Asset price bubbles: economics, mathematics and statistics

Cours Bachelier, Institute Henri Poincare - Winter 2010


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Course Description

Starting with the economic literature, we will review the most common models explaining the appearance of bubbles in asset prices. These are market equilibrium models where some kind of restriction (say short selling constraints) limit the ability of arbitrageurs to profit from and eliminate bubbles. We then move to the characterization of bubbles in the mathematical finance literature, based on the notion of NFLVR (no-free-lunch-with-vanishing risk) and using the concepts of strict local martingales and Merton's no-dominance. We conclude by describing some of the statistical methods that have been proposed to detect the existence of a bubble for an asset and its corresponding derivatives.

Schedule and References

            - Bubbles, rational expectations, and financial markets, O. Blanchard and M.W. Watson, in Crises in the Economic and Financial Structure. Lexington Books (1982).
            - The Theory of Rational Bubbles in Stock Prices, B. T. Diba and H. I. Grossman, The Economic Journal, Vol. 98, No. 392, pp. 746-754 (1988).
            - On the Possibility of Speculation under Rational Expectations, J.Tirole, Econometrica, Vol. 50, No. 5, pp. 1163-1181(1982).
            - Asset Bubbles and Overlapping Generations, J. Tirole, Econometrica, Vol. 53, No. 6, pp. 1499-1528 (1985).
            - Stock prices and social dynamics, R. J. Shiller, Cowles Foundation Discussion Papers, No. 719R (1984).
            - Noise Trader Risk in Financial Markets, J. B. DeLong,  A. Shleifer, L.H. Summers and R. J. Waldmann, The Journal of Political Economy, Vol. 98, No. 4, pp. pp. 703-738 (1990).
            - The Limits of Arbitrage, A. Shleifer and R. W. Vishny, The Journal of Finance, Vol. 52, No. 1, pp. 35-55 (1997).
            - Bubbles and Crises, F. Allen and D. Gale, The Economic Journal, Vol. 110, No. 460, pp. 236-255 (2000).
           - Speculative Investor Behavior in a Stock Market with Heterogeneous Expectations, J. M. Harrison and D. M. Kreps, The Quarterly Journal of Economics, Vol. 92, No.2, pp. 323-336 (1978).
            - Overconfidence and Speculative Bubbles, J. A. Scheinkman and W. Xiong, The Journal of Political Economy, Vol. 111, No. 6, pp. 1183-1219 (2003).
            - Asset Price Bubbles in Complete Markets, R. A. Jarrow, P. Protter, and K. Shimbo, in Advances in Mathematical Finance. Birkhäuser Boston (2007).
            - Asset Price Bubbles in Incomplete Markets, R. A. Jarrow, P. Protter, and K. Shimbo, Mathematical Finance, Vol 20, No. 2, pp. 145-185 (2010).
            - Bubbles and Fads in Asset Prices, C. Camerer, Journal of Economic Surveys, Vol 3, No. 1, pp. 3-41 (1989).
           - Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?, R. J. Shiller, American Economic Review, Vol 71, No. 3, 421-436 (1981).
            - Tulipmania, P. Garber, Journal of Political Economy, Vol 97, No. 3, pp. 535-560 (1989).
            - Famous First Bubbles, P. Garber, Journal of Economic Perspectives, Vol 4, No. 2, pp. 35-54 (1990).
            - The stock market bubble of 1929: evidence from clsoed-end mutual funds, J. B. De Long and A. Shleifer, The Journal of Economic History, Vol 51, No. 3, 657-700 (1991).