On February 5, 2018, the VIX (CBOE Volatility Index) jumped from 17 to 37 in a single trading session, a 115% move. Two products built on selling VIX futures, XIV and SVXY, were mathematically designed to handle moves up to about 80% before triggering liquidation. The jump exceeded that threshold. Credit Suisse's XIV product auto-liquidated, losing investors $2 billion overnight. ProShares' SVXY survived but lost 90% of its value in one day.
Measures of volatility. Three primary measures operate at different points in time.
Historical (realized) volatility. Annualized standard deviation of past returns. The intuition: take daily log returns, square their deviations from the mean, average, and scale to annual. Squaring deviations penalizes outliers and forces every move to count as risk regardless of sign; the factor of 252 converts daily variance to annual because there are roughly 252 trading days in a year. Shorter windows react faster but carry more noise; longer windows smooth through regimes but miss recent shifts.
Common mistakes
- Assuming all long options are long volatility. Vega is a partial derivative (positive for any long simple option); long or short volatility is an empirical correlation. A long equity index has zero vega yet is short volatility, and a deep ITM index call has positive vega yet is short volatility because its delta dominates.
- Confusing vega peak and gamma peak. Both peak ATM, but vega peaks for long-dated options while gamma peaks for short-dated. Trap answer: claims gamma is highest for long-dated ATM (true for vega, false for gamma).
- Treating implied vol as a forecast of realized vol. Implied vol = expected realized vol + vol risk premium. For equity indices, implied runs 2-4 points above realized on average. Trap answer: sets expected realized = implied.
Bottom line
- Realized volatility carries three limitations: it conveys no distribution shape, no trend or mean-reversion information, and no price or time clustering information.
- Sinclair's six properties: volatility clusters (not constant), stays low then jumps, short swings mean-revert, higher vol raises risk aversion, rises in bear and falls in bull, and rises faster than it falls.
- Vega has a textbook form and a per-basis-point form (divide by 100); for finite shifts .
- Every long simple option has positive vega, but that is not the same as long volatility (a deep ITM index call shows positive vega while its delta makes it short volatility).
Exam shortcut
DECISION: Greek questions: ATM + long-dated → vega story. ATM + short-dated → gamma and theta story. Deep OTM/ITM → neither peaks there. Fast lookups the exam rewards: Vega highest? ATM, long-dated. Gamma highest? ATM, short-dated. Vega per basis point? Textbook vega ÷ 100; finite shift Δp ≈ ν·Δσ. Call vega vs put vega? Equal (put-call parity: Stock − Bond has zero vega). Positive vega but short vol?
The full lesson (about 6,572 words, 44 min read) adds 2 worked examples, all 7 common mistakes, a self-check, free in the app.
Learning objectives
- measures volatility
- vega gamma theta
- vol as factor
- modeling vol processes
- implied vol structures
- option strategies vol
- delta neutral vol
- variance vol derivatives
- correlation dispersion
- vol correlation summary
- uncertainty ambiguity opacity
- asset strategy complexity
- complexity perverse incentives
- structured products wrappers
- exotic option features
- eusipa classification
- global structured cases
- structured product valuation
- currency hedging re
- currency risk perfect markets
- currency risk alts
- futures quanto
- intl re overview
- intl re challenges
- crypto investment styles
- crypto fund strategies
- crypto trading strategies
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