Historical Volatility

Name Type Prerequisite Use Cases
Historical Volatility (HV) Volatility StdDev Assesses the historical risk profile and prices options.

Definition

Historical Volatility (HV) is a statistical measure of the dispersion of returns for a given security or market index over a given period of time. Generally, this measure is calculated by determining the standard deviation of the logarithmic returns.

Mathematical Equation

  1. Calculate Log Returns: \(r_t = \ln(P_t / P_{t-1})\).

  2. Calculate Standard Deviation of \(r\) over \(N\) periods: \(\sigma\).

  3. Annualize: \(HV = \sigma \times \sqrt{252} \times 100\).

Special cases

  • Maximum possible value: Unbounded
  • Minimum possible value: 0
  • Behavior: Moves independently, measuring the standard deviation of logarithmic returns over a period.

Visualization

Historical Volatility

Trading Significance

  1. Risk Assessment: Higher volatility implies higher risk.

  2. Option Pricing: It is a key input in option pricing models like Black-Scholes.

  3. Breakout: Low historical volatility often precedes a breakout.