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

Medium
Black-ScholesRisk-Neutral PricingDelta HedgingGreeksGBM
02

The Equity Volatility Smile

Medium
Volatility SmileImplied VolatilitySkewVol SurfaceRisk ReversalBreeden-Litzenberger
03

Dupire Local Volatility

Hard
Local VolatilityDupire FormulaImplied Vol SurfaceForward Kolmogorov EquationSmile Dynamics
04

The Heston Stochastic Volatility Model

Hard
Heston ModelStochastic VolatilityCIR ProcessCharacteristic FunctionVol of VolCorrelationSmile Dynamics
05

Barrier Options — Pricing and Risk

Hard
Barrier OptionsKnock-InKnock-OutReflection PrincipleBlack-Scholes Barrier FormulaGreeksVannaSmile Adjustment
06

Exotic Equity Payoffs

Hard
Asian OptionsLookback OptionsVariance SwapsVolatility SwapsCliquetsCorridor VarianceDigital OptionsGap Risk