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While the use of volatilities is pervasive throughout finance, our ability todetermine the instantaneous volatility of stocks is nascent. Here, we present amethod for measuring the temporal behavior of stocks, and show that stockprices for 24 DJIA stocks follow a stochastic process that describes anefficiently priced stock while using a volatility that changesdeterministically with time. We find that the often observed, abnormally largekurtoses are due to temporal variations in the volatility. Our method canresolve changes in volatility and drift of the stocks as fast as a single dayusing daily close prices.

Volatilities That Change with Time: The Temporal Behavior of the Distribution of Stock-Market Prices