Cluster D: Volatility
The most important concept in options. From basic implied vol through the volatility surface to stochastic and local volatility models.
What Is Volatility
Historical (realized) vol vs implied vol, annualization, why volatility matters more than direction for options
Implied Volatility: Market's Forecast
IV as the market-clearing input, IV crush around events, IV percentile and IV rank
The Volatility Smile and Skew
Why BSM predicts flat vol but markets show skew, demand-driven skew, crash protection premium, risk reversal
Term Structure of Volatility
Front-month vs back-month IV, contango vs backwardation in vol, calendar spread implications
The Volatility Surface
3D surface (strike x expiry x IV), parameterization (SVI, SABR), interpolation challenges
VIX and Volatility Products
VIX construction methodology, VIX futures, term structure, volatility ETPs, vol-of-vol
Realized Volatility Measurement
Close-to-close, Parkinson, Garman-Klass, Yang-Zhang estimators, sampling frequency effects
Stochastic Volatility Models
Heston model, SABR, mean reversion in vol, calibration to market surfaces, smile dynamics
Local Volatility and Dupire's Equation
Local vol as a deterministic function, Dupire formula, strengths and weaknesses vs stochastic vol
Variance Swaps and Volatility Derivatives
Variance swap replication, vol swap convexity adjustment, corridor variance swaps
Earnings and Event Volatility
IV behavior around binary events, earnings vol premium, straddle pricing for events, post-event IV crush mechanics