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

TL;DR

This paper introduces a method to measure the time-varying volatility of stocks, revealing that observed kurtoses are due to deterministic changes in volatility, and can detect daily changes in stock behavior.

Contribution

It presents a novel approach for tracking the instantaneous, deterministic changes in stock volatility and drift using daily closing prices.

Findings

Stock prices follow a stochastic process with time-dependent volatility.

Large kurtoses are caused by temporal variations in volatility.

The method detects daily changes in volatility and drift.

Abstract

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.