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

While the use of volatilities is pervasive throughout finance, our ability to determine the instantaneous volatility of stocks is nascent. Here, we present a method for measuring the temporal behavior of stocks, and show that stock prices for 24 DJIA stocks follow a stochastic process that describes an efficiently priced stock while using a volatility that changes deterministically with time. We find that the often observed, abnormally large kurtoses are due to temporal variations in the volatility. Our method can resolve changes in volatility and drift of the stocks as fast as a single day using daily close prices.