Equity Derivatives Pricing
Black-Scholes and its structural failures, implied vol surfaces, local vol (Dupire), stochastic vol (Heston, SABR, rough vol), barrier options, and variance swaps — from closed-form to full numerical implementation.
6 modules~163 min total
Prerequisites
Stochastic Calculus & SDEsNumerical Methods (Monte Carlo, finite differences)C++ or Python (working knowledge)
Modules
01
The Black-Scholes Model
MediumBlack-ScholesRisk-Neutral PricingDelta HedgingGreeksGBM
02
The Equity Volatility Smile
MediumVolatility SmileImplied VolatilitySkewVol SurfaceRisk ReversalBreeden-Litzenberger
03
Dupire Local Volatility
HardLocal VolatilityDupire FormulaImplied Vol SurfaceForward Kolmogorov EquationSmile Dynamics
04
The Heston Stochastic Volatility Model
HardHeston ModelStochastic VolatilityCIR ProcessCharacteristic FunctionVol of VolCorrelationSmile Dynamics
05
Barrier Options — Pricing and Risk
HardBarrier OptionsKnock-InKnock-OutReflection PrincipleBlack-Scholes Barrier FormulaGreeksVannaSmile Adjustment
06
Exotic Equity Payoffs
HardAsian OptionsLookback OptionsVariance SwapsVolatility SwapsCliquetsCorridor VarianceDigital OptionsGap Risk