84553 - Financial Mathematics

Academic Year 2023/2024

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Economics and Finance (cod. 8835)

Learning outcomes

The aim of the course is to provide the mathematics of the fundamental laws governing financial contracts. In particular, the course covers the different types of interest to compute present and accumulated values for different streams of cash flows. Applications include annuities, debt retirement methods, mortgages, bond and stock pricing, capital budgeting and the valuation of contingent claims.

Course contents

  1. Description of financial products: cash-flows, coupons, amortizing schedules.
  2. Compounding and discount operations. Returns and interest rates.
  3. Annuities and amortizing schedules
  4. Forward rates and floating rate notes
  5. Swap contracts and swap rates
  6. Bond and swap markets: term structure analysis
  7. Duration and convexity
  8. Investing and funding at floating and fixed rates
  9. Immunization theorems
  10. Spreads (Z-spread and Asset Swap Spread)
  11. Default intensity and CDS
  12. Introduction to options
  13. Option pricing: the binomial model
  14. Option pricing: the risk-neutral measure price
  15. Introduction to the continuous time model
  16. The Black and Scholes model
  17. Implied volatility and VIX
  18. Introduction to APT (arbitrage pricing theory)
  19. Introduction to portfolio theory: mean-variance analysis
  20. Fund separation theorems and management

Readings/Bibliography

Lecture notes and selected readings.

Teaching methods

Lectures

Assessment methods

The assessment will consist of a written exam with:

1. A set of questions with multiple answers covering all the material in the course.

2. A specific problem to be discussed or solved.

Oral examination can be requested by, in which case the grade could be raised or decreased depending on the performance. The object of the oral examination will not be limited to the topic addressed in the written exam, but will extend to all the material covered during the course.

The maximum possible score is 30 cum laude.

The grades are described as follows

< 18 failed

18-23 sufficient

24-27 good

28-30 very good

30 cum laude Excellent

Teaching tools

Exercises in Excel VBA and (very introductory) Python

Office hours

See the website of Umberto Cherubini