---
description: "Background on volatility as an asset class: historical vs. implied volatility, VIX as the market's fear gauge, and the spectrum of instruments (options, futures, ETNs) used for volatility trading."
tags: [volatility, background, vix, implied-volatility, options]
---

# Volatility Generalities

**Section**: 7.1 | **Asset Class**: Volatility | **Type**: Background / Reference

## Overview
Volatility can be viewed as an asset class in its own right. Volatility strategies make bets on whether future realized volatility will be higher or lower, or on the relationship between implied and realized volatility. Volatility is measured historically (from past returns) or implied (extracted from option prices, forward-looking). VIX is the dominant index-level volatility measure and its derivatives provide direct trading vehicles.

## Construction / Mechanics

### Historical (Realized) Volatility
Based on a time series of past returns. For daily log-returns R(t) = ln[S(t)/S(t-1)] over a window of T days:
```
σ_realized = sqrt(F/T · Σ_{t=1}^T R(t)²)
```
where F = 252 (annualization factor for daily data). Note: mean is not subtracted (consistent with variance swap conventions).

### Implied Volatility
Extracted from option prices via the Black-Scholes formula or model-free methods. Implied volatility is forward-looking: it represents the market's expectation of future volatility over the option's lifetime.

### VIX
The CBOE Volatility Index (VIX), the "fear gauge" or "uncertainty index," measures the market's expectation of 30-day volatility of the S&P 500 as implied by a range of S&P 500 options. Related indexes include:
- **RVX**: CBOE Russell 2000 Volatility Index
- **VXEEM**: CBOE Emerging Markets ETF Volatility Index
- **TYVIX**: CBOE/CBOT 10-year U.S. Treasury Note Volatility Index
- **GVZ**: CBOE Gold ETF Volatility Index
- **EUVIX**: CBOE/CME FX Euro Volatility Index

### Volatility Trading Instruments
- **Options**: direct vol exposure, but require Delta-hedging to isolate volatility (see Section 7.4.1)
- **VIX futures (UX1, UX2, ...)**: UX1 ≈ 1 month to maturity; allow direct trading of forward implied vol
- **Volatility ETNs**: VXX tracks short-maturity VIX futures (months 1-2); VXZ tracks medium-maturity (months 4-7); subject to roll/contango losses
- **Variance swaps**: payoff proportional to realized variance minus strike; no Delta-hedging required (see Section 7.6)

## Key Concepts
- **Volatility risk premium**: implied vol > realized vol most of the time; selling volatility is structurally profitable on average but with crash risk
- **Contango**: VIX futures curve upward-sloping (most common); VXX loses value via roll loss
- **Backwardation**: VIX futures curve downward-sloping (during stress); VXX gains from roll
- **VIX and equities are anti-correlated**: VIX typically spikes during equity market selloffs

## Notes
- Options-based volatility strategies (straddles, etc.) are covered in Section 2 of the book; this chapter focuses on VIX derivatives and variance swaps.
- Long volatility positions profit in crises (natural hedge) but are expensive to maintain due to roll/theta decay.
- Short volatility positions earn the volatility risk premium in normal markets but suffer catastrophic losses during sudden vol spikes.