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Stochastic Calculus & Derivative Pricing Theory.

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10FAMILIES
94PAGES
2CAREERS USE IT

From Brownian motion to calibration.

Ω SAMPLE SPACEF SIGMA-ALGEBRAP MEASURE

Probability Foundations

The Probability SpaceSigma-Algebra
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PATHDRIFT

Stochastic Processes and Jumps

MartingaleBrownian Motion and Its Properties
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RIEMANNITO
WHEN THE PATH IS RANDOM

Ito Calculus

The Ito IntegralThe Ito Integral vs the Riemann Integral
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Stochastic Differential Equations

dS = DRIFT + DIFFUSION
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PQ
PHYSICAL VS RISK-NEUTRAL

Pricing Theory and No-Arbitrage

No-ArbitragePhysical and Risk-Neutral Measures
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BLACK-SCHOLES

Option Pricing Theory

European and American OptionsThe Black-Scholes PDE
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CONSTANTLOCALHESTONSABRCIR

Volatility Models

Constant, Local and Stochastic VolatilityThe Heston Model
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RATEMEAN

Interest Rate Models

Mean ReversionThe Zero-Coupon Bond
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SIMULATEDISCOUNTAVERAGE

Numerical Pricing

Monte Carlo PricingEuler and Milstein Schemes
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MARKET
MODEL

Calibration and Model Risk

CalibrationMarket Price and Model Price
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Probability FoundationsCOREStochastic Processes and JumpsCOREIto CalculusCOREStochastic Differential EquationsCOREPricing Theory and No-ArbitrageCOREOption Pricing TheoryCOREVolatility ModelsCOREInterest Rate ModelsCORENumerical PricingCORECalibration and Model RiskCORE
THIS CAREER NEEDSQuant Analyst
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BOOTCAMPQuant AnalystModels, simulation and pricing. In code.INTERNSHIP CERT.RECOMMENDATIONSee the curriculum
FREE COURSESThe Greeks, PracticallyReading an Option PayoffRegression for Finance