Observability of Market Daily Volatility

TL;DR

This paper demonstrates that it is possible to directly observe and define daily market volatility from data, moving beyond traditional indirect methods, by utilizing comprehensive market information.

Contribution

It introduces a method to operatively define and detect daily market volatility directly from market data, unlike traditional indirect approaches.

Findings

Daily market volatility can be directly observed from data.

The traditional relation r(t)=σ(t)ω(t) is insufficient for defining volatility.

A new approach uses full market information to detect volatility.

Abstract

We study the price dynamics of 65 stocks from the Dow Jones Composite Average from 1973 until 2014. We show that it is possible to define a Daily Market Volatility $\sigma(t)$ which is directly observable from data. This quantity is usually indirectly defined by $r(t)=\sigma(t) \omega(t)$ where the $r(t)$ are the daily returns of the market index and the $\omega(t)$ are i.i.d. random variables with vanishing average and unitary variance. The relation $r(t)=\sigma(t) \omega(t)$ alone is unable to give an operative definition of the index volatility, which remains unobservable. On the contrary, we show that using the whole information available in the market, the index volatility can be operatively defined and detected.