Probability Theory

This module comes first because probability theory is the language in which modern finance is written. Every pricing formula is an expectation. Every risk measure is a quantile or a variance. Every simulation is a draw from a distribution. Without a rigorous probability foundation, derivatives pricing is hand-waving, risk models are black boxes, and Monte Carlo is a prayer.

You’ve used these tools in practice --- regression at Credimi, yield curve optimization at Gottex --- but the theory is fuzzy. This module makes it rigorous.

Dependency Graph

Probability theory (Module 0.1) feeds everything downstream:

0.1 Probability Theory
 ├──→ 0.2 Stochastic Processes & Stochastic Calculus
 ├──→ 0.3 Statistics & Estimation
 │     └──→ 0.4 Econometrics
 └──→ unlocks:
       • Black-Scholes & risk-neutral pricing (derivatives pricing)
       • Term structure models (Vasicek, CIR, HJM)
       • Credit risk (PD, LGD, Basel)
       • Portfolio theory (Markowitz, CAPM)
       • Monte Carlo simulation

Within this module, the articles build on each other:

0.1.1 Sample Spaces & σ-Algebras
  └──→ 0.1.2 Probability Measures & Axioms
        └──→ 0.1.3 Random Variables & Distributions
              └──→ 0.1.4 Expectation, Variance & MGFs
                    └──→ 0.1.5 Joint Distributions & Independence
                          └──→ 0.1.6 Conditional Expectation
                                └──→ 0.1.7 LLN & CLT

Learning Roadmap

Articles 0.1.2 through 0.1.7 are roadmaps --- their content will be developed in future sessions. Article 0.1.1 is complete and ready for study.