Martingale-Like Behavior of Prices
Asset prices set in a competitive market need not be martingales; that is, it need not be true that the best predictor of future prices is the current price. Nonetheless, statistical tests for this property are sometimes treated as tests for the proper functioning of an asset market; asset prices often seem to have the property to a close approximation, and it is sometimes supposed that the martingale ought to be imposed on econometric models of asset markets and forecasts made from them. This paper shows that under general conditions, which allow among other things for risk aversion among market participants, competitive asset prices ought to be locally -- over small units of time -- martingale-like. This implies that tests of proper functioning of the market ought to be conducted with data at fine time intervals; results of such tests should not be used to justify imposing the martingale property on a model's long-term projections of asset prices.
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- Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- LeRoy, Stephen F, 1973. "Risk Aversion and the Martingale Property of Stock Prices," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 436-46, June.
- Ross, Stephen A, 1978. "A Simple Approach to the Valuation of Risky Streams," The Journal of Business, University of Chicago Press, vol. 51(3), pages 453-75, July.
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