This is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximization, and maybe other topics. We prove the fundamental theorem of asset pricing and the hedging duality theorems in discrete time, and also study convex duality in utility maximization.
In addition, programming exercises will be given in Python (2.7), each week. www.python.org. For any question, the assistants of the financial mathematics group will be available for you during the assistant hours, see praesenz.
| Dates | Week | Topic | Exercise sheet | Solutions | Python |
|---|---|---|---|---|---|
| 20 February | 1 | Dynamic arbitrage theory (ch 5) | presentation | Introduction to Python slides | Introduction python |
| 27 February | 2 |
European Contingent Claims (ch 5.3)
Complete Markets (ch 5.4) |
es 1 py 1 |
sol 1 sol py 1 |
Black Scholes closed formula for a call option |
| 6 March | 3 |
The Fundamental Theorem of Asset Pricing (ch 1.6) |
es 2 py 2 |
sol 2 sol py 2 imf_ex2_claudio_segovia imf_ex2_manvir_schneider |
Black Scholes closed formula for a put option Monte Carlo pricer for call and put options |
| 13 March | 4 |
European Contingent Claims (ch 5.3) Complete Markets(ch 5.4) The binomial Model (ch 5.5) |
es 3 py 3 |
sol 3 imf03_florian_krach.pdf sol py 3 imf_ex3_manvir_schneider imf_ex3_tobias_wyss |
Option price properties Call Put parity |
| 20 March | 5 | arbitrage.tm using TeXmacs
The binomial Model (ch 5.5) The Numeraire change theorem |
es 4
py 4 |
sol 4
sol py 4 imf_ex4_tobias_ruckstuhl |
Binomial model |
| 27 March | 6 | Exotic Derivatives (ch 5.6) Convergence to the Black Scholes price (ch 5.7) American contingent claims (ch 6) |
es 5
py 5 |
sol 5
sol py 5 imf_ex5_florian_krach |
Binomial model Path dependent pricing |
| 3 April | 7 |
American contingent claims (ch 6) Hedging strategy for the seller (ch 6.1) Stopping strategies for the buyer (ch 6.1) Examples of optimal stopping times |
es 6
py 6 |
sol 6
Corinne_Emmenegger.pdf sol py 6 imf06_Claudio_Segovia.pdf imf06_florian_krach.pdf |
Trinomial model |
| 10 April | 8 | American contingent claims (ch 6) Arbitrage-free prices (ch 6.3) |
es 7 | sol 7
imf07_tobias_wyss.pdf imf_ex07_armin_fingerle |
Trinomial model Path dependent pricing |
24 April | 9 | Arbitrage-free prices (ch 6.3) Stability under pasting (ch 6.4) |
es 8 py 8 |
sol 8 sol py 8 | American pricing with binomial and trinomial model | 1 Mai | 10 | Lower and upper Snell envelopes (ch 6.5) | es 9 | sol 9
corinne_emmenegger.pdf imf09_florian_krach.pdf |
American pricing with binomial and trinomial model Comparison with American Monte Carlo |
8 Mai | 11 | Utility Optimization (lecture notes) | es 10 | sol 10
imf09_florian_krach.pdf imf10_manvir_schneider.pdf |
15 Mai | 12 | Utility Optimization | es 11 | sol 11 | 22 Mai | 13 | Monetary measure of risk (ch 4) | es 12 | sol 12 | 29 Mai | 14 | Monetary measure of risk (ch 4) | es 13 | sol 13
imf13_corinne_emmenegger.pdf imf13_florian_krach.pdf imf13_moritz_weiss.pdf |
| Class | Time | Room | Responsibles |
|---|---|---|---|
| Cours | Monday 14:15 - 16:00 | HG D1.1 | Prof. Josef Teichmann |
| Cours | Thursday 08:15 - 10:00 | ML F 36 | Prof. Josef Teichmann |
| Exercises | Wednesday 15:15 - 16:00 | HG E 21 | Prof. Josef Teichmann and Calypso Herrera |
For the oral exam I shall choose randomly three questions from the following
list, from which you have the right to select two for your exam.You will have about 10 minutes of time for each question after about 10
minutes of preparation. I expect you to speak about the question like in a seminar,
i.e. explaining the structure of the answer and important details such that a good
mathematician, who does not know precisely about the topic could in principle
follow.
Notice that the exam is “open book”, i.e. you can use the book of Föllmer-Schied during the preparation of the answers to the randomly chosen questions. Notice, however, that I ask very detailed questions. An oral exam is a pleasant scientific discussion, it is all about understanding. If you have any questions, please do not hesitate to contact me.
(1) the book of FS and my lecture notes will be available in my office for the exam. To guarantee equal conditions no personal notes are allowed.
(3) of course you can make notes on a sheet of paper during preparation, but then we switch to a fresh piece of paper.
The catalogue of questions for the oral exam at the end of the lecture notes.
Prof. Josef Teichmann.