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Volatility & Surfaces

Implied vol, SVI/SSVI/SABR, Heston, rough vol.

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Heston: stochastic volatility's first closed form

recommend Itô's lemma: where the half-sigma-squared comes from +3 more first

Hurst exponent: measuring roughness of a process

recommend Random walk: gambler's ruin and hitting probabilities +2 more first

Static arb-free constraints: butterfly, calendar, no-negative-density

recommend Arbitrage: when prices have to agree, or you get paid +2 more first

Bergomi: forward variance as the modelling primitive

recommend Variance swaps via static replication +3 more first

fBM via Volterra kernel: where roughness comes from

recommend Hurst exponent: measuring roughness of a process +2 more first

Lee moment formula: how steep can a vol wing be?

recommend Static arb-free constraints: butterfly, calendar, no-negative-density +2 more first

Rough Bergomi: when the kernel is fractional

recommend Bergomi: forward variance as the modelling primitive +3 more first

SVI (Stochastic Volatility Inspired): Gatheral's 5-parameter slice fit

recommend Static arb-free constraints: butterfly, calendar, no-negative-density +2 more first

Vega-weighted calibration: why fit vols, not prices

recommend SVI (Stochastic Volatility Inspired): Gatheral's 5-parameter slice fit +1 more first

SABR (Stochastic Alpha Beta Rho): joint diffusion of forward and vol

recommend SVI (Stochastic Volatility Inspired): Gatheral's 5-parameter slice fit +3 more first

SSVI: SVI extended to the whole surface

recommend SVI (Stochastic Volatility Inspired): Gatheral's 5-parameter slice fit +2 more first

Fengler: non-parametric arb-free vol surface smoothing via Quadratic Programming (QP)

recommend Static arb-free constraints: butterfly, calendar, no-negative-density +2 more first