⚡ QUICK ANSWER: What is Gatheral SVI Volatility Skew?
The Gatheral SVI (Stochastic Volatility Inspired) Model is a 5-parameter mathematical model ($a, b, \rho, m, \sigma$) that fits total implied variance across option strike prices. It accurately captures real-market Put Skew (higher IV on downside strikes) while guaranteeing that fitted volatility curves remain free of butterfly and calendar arbitrage.
1. The Gatheral SVI Formulation
Gatheral's raw SVI formulation expresses total variance $w(k) = \sigma_{impl}^2 T$ as a function of log-moneyness $k = \ln(K / F)$:
w(k) = a + b * [ ρ * (k - m) + √((k - m)² + σ²) ]
- $a$: Overall variance level offset.
- $b$: Slope/angle of the volatility wings.
- $\rho$: Rotation/skew parameter measuring put-vs-call asymmetry.
- $m$: Horizontal shift parameter centering the ATM minimum.
- $\sigma$: Smoothness/curvature parameter at the ATM dip.
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