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Introduction

Quantitative finance is an exciting field where we apply mathematics, statistics, and computing to solve financial problems. The main finance areas where advanced quantitative techniques are applied are derivative securities (pricing and hedging), risk management, and portfolio management. This course introduces the fundamental mathematical and statistical tools of quantitative finance in a rigorous way and with applications. The core aims are the analysis of financial variables, the modeling of uncertainty and risk, and the building of market models for pricing and portfolio choices.

Course content

Subject to time constraints, the course will cover the following topics:

1. A review of basic mathematics, including probability theory, statistics, linear algebra, and calculus.
2. The time-value of money.
3. Probability distributions.
4. Bayesian analysis.
5. Hypothesis testing.
6. Linear algebra and vector spaces.
7. Regression analysis.
8. Time series models.
9. Safe and risky assets.
10. Discrete time market models.