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Probability and Math Finance Seminar
Albina Danilova, Carnegie Mellon UniversityUnderstanding Stochastic Volatility AbstractIn this talk I will present a sequential trading model, with asymmetric information, that provides a theoretical rationalization of the empirical evidence on the link between volume of trade and stock price movements. In the first half of the talk, based on the joint work with Rene Carmona, I will show that if there is no transaction cost in the market, the geometric Brownian motion model of asset prices is consistent with agents? learning and asymmetric information. I would also provide empirical support for the theoretical implication of our model that trading volume drives the price process: indeed, at very high frequency, the volume of trade is able to explain more then one third of the variability in asset returns. In the second half of the talk, based on joint work with Christian Julliard, I will present an extension of the above model which includes transaction costs, and demonstrate that, although the role of volume of trades in stock price formation does not change, the information content of number of trades changes dramatically: in this setting, as the intensity of agents? arrival goes to infinity, the stock price process converges to the time changed geometric Brownian motion, with the time change given by the number of trades. That is, in this model stochastic volatility endogenously arises from the strategic interaction of agents with heterogeneous information. Moreover, I document strong empirical support for this theoretical result. MONDAY, September 22, 2008 |