Understanding the CBOE VIX Methodology

Academic resource for PhD researchers implementing and analyzing the volatility index

Interactive Calculator Learn Methodology

Project Overview

VIX Calculator

Complete implementation of CBOE's variance swap methodology with step-by-step breakdown

Synthetic Data

Generate realistic option chains for 5 market regimes: normal, high vol, crisis, low vol, skew shock

Realized Volatility

5 estimators: Close-to-Close, Parkinson, Garman-Klass, Yang-Zhang, Rogers-Satchell

VIX Derivatives

Futures term structure, contango/backwardation analysis, VVIX calculation

VIX Calculation Methodology

The Variance Swap Formula

The VIX is calculated using a variance swap approach that is model-free:

\[\sigma^2 = \frac{2}{T} \sum_i \frac{\Delta K_i}{K_i^2} e^{RT} Q(K_i) - \frac{1}{T}\left[\frac{F}{K_0} - 1\right]^2\]

Where:

  • T = Time to expiration (in years)
  • F = Forward index level derived from option prices
  • K0 = First strike below the forward price
  • Ki = Strike price of i-th out-of-the-money option
  • ΔKi = Interval between strike prices
  • R = Risk-free interest rate
  • Q(Ki) = Midpoint of bid-ask spread for option with strike Ki

Calculation Steps

1

Select Options

Choose near-term and next-term SPX options with expirations bracketing 30 days

2

Calculate Time

Compute time to expiration in minutes for precision

3

Find Forward Price

Use put-call parity: F = K + eRT(Call - Put)

4

Select Strikes

Use OTM puts below K0, OTM calls above K0

5

Calculate Contributions

Sum weighted option prices using variance formula

6

Interpolate

Interpolate to 30-day constant maturity

Final VIX:

\[VIX = 100 \times \sqrt{\sigma^2_{30-day}}\]

Key Visualizations

View All Interactive Charts

Contribution by Strike

Shows how each strike contributes to VIX variance

Volatility Smile

Implied volatility across strikes showing equity skew

30-Day Interpolation

Near/next term weighting for constant maturity

Futures Term Structure

Contango and backwardation patterns

Variance Risk Premium

VIX vs realized volatility analysis

VVIX Relationship

Volatility of volatility analysis

References

  • CBOE (2019). VIX White Paper. Chicago Board Options Exchange.
  • Carr, P., & Madan, D. (1998). Towards a theory of volatility trading. Volatility: New Estimation Techniques for Pricing Derivatives.
  • Demeterfi, K., Derman, E., Kamal, M., & Zou, J. (1999). More than you ever wanted to know about volatility swaps. Goldman Sachs Quantitative Strategies Research Notes.