VIX Index

The VIX is calculated using a model-free implied volatility formula derived from a wide strip of near-term and next-term S&P 500 Index (SPX) options. Unlike Black-Scholes implied volatility, it does not assume a specific options pricing model.

• Aggregates out-of-the-money puts and calls weighted by their contribution to variance.
• Uses a discrete approximation of the fair value of a variance swap.
• The calculation isolates the 30-day forward-looking expectation by interpolating between two expiration cycles.

The VIX exhibits a strong asymmetric negative correlation with the S&P 500. The index tends to spike violently during equity market sell-offs and drift lower during gradual rallies.

• Downside Beta: VIX movements are typically 3-4x larger when SPX falls compared to equivalent SPX gains.
• This behavior stems from the leverage effect and the demand for protective puts during market stress.
• This asymmetry makes VIX derivatives popular for tail-risk hedging.

Unlike equities which trend over the long term, the VIX is a stationary, mean-reverting process. It oscillates around a long-term historical average, typically between 19 and 20.

• High VIX levels signal panic and are unsustainable, eventually reverting as markets calm.
• Low VIX levels signal complacency but can persist for extended periods before a volatility shock.
• This property is the foundation of volatility arbitrage and VIX futures term structure trading.

The VIX itself is a spot index, but VIX futures create a term structure reflecting expectations of future volatility. In normal market conditions, this curve is in contango.

• Contango: Longer-dated futures are more expensive than near-term futures, causing a negative roll yield for long positions.
• Backwardation: Occurs during crises when near-term fear exceeds long-term uncertainty, creating a downward-sloping curve.
• The shape of the curve is a critical input for VIX Exchange-Traded Products (ETPs).

A critical technical nuance is that the VIX calculation squares the expected volatility to derive a variance figure, then takes the square root to quote the index in percentage points.

• The index represents the risk-neutral expected variance of the S&P 500 over 30 days.
• Because variance is not linearly additive, the VIX is not a simple average of component volatilities.
• This non-linearity has significant implications for pricing VIX options and futures, which have convexity exposure to variance.

Exchange-traded derivatives that allow investors to take a position on the expected value of the VIX Index at a future expiration date. Unlike equity futures, VIX futures are priced off the forward implied volatility, not the spot VIX level.

• The VIX futures curve typically exhibits contango (upward sloping) in calm markets due to the volatility risk premium.
• During market stress, the curve can flip into backwardation, where near-term futures trade above longer-dated contracts.
• Settlement is based on a Special Opening Quotation (SOQ) of the VIX Index on the expiration morning.

Options on the VIX Index that provide exposure to the volatility of volatility. These are cash-settled European-style options whose underlying is the VIX Index itself.

• Pricing VIX options requires modeling the vol-of-vol, as the underlying is already a volatility measure.
• The VIX option implied volatility surface often displays a pronounced smile, reflecting demand for out-of-the-money calls as tail-risk hedges.
• Traders use VIX calls to hedge against convexity events where equity volatility spikes rapidly.

The VIX of VIX — a measure of the expected 30-day volatility of the VIX Index itself, derived from VIX option prices. It quantifies the market's expectation of volatility-of-volatility.

• A high VVIX reading indicates uncertainty about future volatility levels, often preceding regime shifts.
• VVIX typically spikes during market dislocations, reflecting demand for VIX options as tail hedges.
• The spread between VVIX and VIX provides insight into the convexity premium embedded in volatility derivatives.

The compensation demanded by option sellers for bearing unhedgeable volatility risk, measured as the difference between implied volatility (VIX) and subsequent realized volatility.

• Historically, the VIX overestimates actual S&P 500 realized volatility by 3-5 percentage points on average.
• This structural premium explains why short volatility strategies have generated positive carry over long horizons.
• The premium collapses or inverts during tail events, when realized volatility spikes above implied levels.

Over-the-counter derivatives that pay the difference between realized variance and a pre-agreed strike variance. Unlike the VIX, which is model-free but discrete, variance swaps provide pure exposure to realized volatility.

• The VIX formula replicates a variance swap payoff under idealized assumptions of continuous monitoring and no jumps.
• The convexity adjustment between VIX and variance swap strikes reflects the impact of discrete sampling and jump risk.
• Market makers use variance swaps to hedge gamma exposure from options portfolios.

The curve representing VIX futures prices across different expiration months, reflecting the market's expectation of forward volatility at various horizons.

• In contango, longer-dated futures trade at a premium, creating a negative roll yield for long positions.
• In backwardation, near-term futures trade higher, typically during acute market stress.
• The slope of the term structure is a key input for volatility carry strategies and VIX exchange-traded product (ETP) pricing.