SC

Stochastic calculus

Brownian motion, Itô calculus and the measure change that makes risk-neutral pricing work.

1
Brownian motion
Defining properties, quadratic variation and the Brownian bridge.
- 1.1Brownian motion: the defining properties and what follows12 min
2
Hitting times
The reflection principle, running maxima and first passage.
- 2.1Hitting times, the reflection principle and the running maximum12 min
3
The Itô integral and Itô’s lemma
Itô isometry, the lemma in one and several dimensions, and the standard computations.
- 3.1Itô’s lemma and the computations you will be asked for15 min
4
SDEs and named processes
Geometric Brownian motion, Ornstein–Uhlenbeck, CIR and Vasicek.
- 4.1SDEs: geometric Brownian motion, Ornstein–Uhlenbeck and the rest12 min
5
Martingales and measure change
Girsanov, Feynman–Kac and the fundamental theorems.
- 5.1Measure change: Girsanov, Feynman–Kac and the fundamental theorems13 min