Stochastic Calculus & Derivative Pricing Theory

F1
Probability Foundations
The formal setting. Probability space, sigma-algebra, measure and expectation.
- 01
  Risk-Neutral Probability: The Weight That Prices, Not a Belief
  Calculate
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
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
  Calculate
- 02
  Black Scholes and the Greeks: Five Sensitivities, Five Units
  Calculate
- 03
  Binomial Option Pricing: Building and Checking the Tree
  Calculate
F7
Volatility Models
Relaxing the constant volatility assumption. Local, stochastic, Heston, SABR.
- 01
  Implied Volatility: The Number Backed Out of a Price
  Calculate