Stochastic Calculus & Derivative Pricing Theory

  1. F1

    Probability Foundations

    The formal setting. Probability space, sigma-algebra, measure and expectation.

    • 01

      Risk-Neutral Probability: The Weight That Prices, Not a Belief

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  2. F5

    Pricing Theory and No-Arbitrage

    The argument. No-arbitrage, the fundamental theorems, measure change and the pricing kernel.

    • 01

      Discount Factors and Zero-Coupon Prices: One Object

      Calculate
  3. F6

    Option Pricing Theory

    The canonical application. Black-Scholes, the binomial model, delta hedging and boundaries.

    • 01

      Monte Carlo European Option: Pricing by Slicing the Odds

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    • 02

      Black Scholes and the Greeks: Five Sensitivities, Five Units

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    • 03

      Binomial Option Pricing: Building and Checking the Tree

      Calculate
  4. F7

    Volatility Models

    Relaxing the constant volatility assumption. Local, stochastic, Heston, SABR.

    • 01

      Implied Volatility: The Number Backed Out of a Price

      Calculate