- Lecturer
- Prof. Dr. Erich Walter Farkas, Prof. Dr. Martin Schweizer
- Coordinator
- Martin Stefanik

This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.

Topics to be covered include

- financial market models in finite discrete time
- absence of arbitrage and martingale measures
- valuation and hedging in complete markets
- basics about Brownian motion
- stochastic integration
- stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem
- Black-Scholes formula

**Lecture notes** that will be closely followed during the lectures will be sold during the break *before* the beginning of the second lecture on September 24 and during the Präsenz hours for CHF20. The lecture notes will *not* be available in electronic form.

Results and facts from measure-theoretic probability theory as given in the book Probability Essentials by Jean Jacod and Philip Protter will be used freely. The book can be downloaded from Springer (within the ETH network or using VPN) for free. Especially participants without a direct mathematical background are strongly advised to familiarise themselves with those tools before (or *very quickly* during) the course.

A possible alternative to the above textbook is the English or German version of the ETH lecture notes for the standard course on *Probability Theory*. These lecture notes can also be purchased during the Präsenz hours.

For those who are not sure about their background, we suggest to have a look at the exercises in Chapters 8, 9, 22-25, 28 in the Probability Essentials book. If these pose problems, you will have a hard time during the course. So be prepared.

Time | Room | Lecturer |
---|---|---|

Monday 13:00-14:00 | HG D 1.1 | usually Prof. Dr. Walter Farkas |

Tuesday 12:00-14:00 | HG D 1.1 | usually Prof. Dr. Walter Farkas |

Time | Room | Assistant | Students |
---|---|---|---|

Friday 08:00-10:00 | HG D 7.1 | Martin Stefanik | A-G |

Friday 08:00-10:00 | LFW E 13 | David Martins | H-O |

Friday 10:00-12:00 | LFW E 13 | Balint Gersey | P-Z |

New exercise sheets will be uploaded here on Tuesdays before the exercise class along with a model solution to the exercise sheet from the previous week.

Note that handing in your solutions is not obligatory, but being able to solve the exercises independently goes a long way towards good exam performance. In case you decide to do so, please hand in your solutions by the following Tuesday 18:00 to your assistant's box next to HG G 53.2. Your solutions will be corrected and returned in the following exercise class or, if not collected, returned to the box next to HG G 53.2.

Exercise sheet | Due by | Solutions |
---|---|---|

Exercise sheet 1 | September 25, 2018 | Solution sheet 1 |

Exercise sheet 2 | October 2, 2018 | Solution sheet 2 |

Exercise sheet 3 | October 9, 2018 | Solution sheet 3 |

Exercise sheet 4 | October 16, 2018 | Solution sheet 4 |

Exercise sheet 5 | October 23, 2018 | Solution sheet 5 |

Exercise sheet 6 | October 30, 2018 | Solution sheet 6 |

Exercise sheet 7 | November 6, 2018 | Solution sheet 7 |

Exercise sheet 8 | November 13, 2018 | Solution sheet 8 |

Exercise sheet 9 | November 20, 2018 | Solution sheet 9 |

Exercise sheet 10 | November 27, 2018 | Solution sheet 10 |

Exercise sheet 11 | December 4, 2018 | Solution sheet 11 |

Exercise sheet 12 | December 11, 2018 | Solution sheet 12 |

Exercise sheet 13 | December 18, 2018 | Solution sheet 13 |

Exercise sheet 14 | NA | Solution sheet 14 |

Exercise class | Material |
---|---|

Exercise 1 (September 21, 2018) | Slides |

Exercise 2 (September 28, 2018) | Slides |

Exercise 3 (October 5, 2018) | Slides |

Exercise 4 (October 12, 2018) | Slides |

Exercise 5 (October 19, 2018) | Slides |

Exercise 6 (October 26, 2018) | Slides |

Exercise 8 (November 9, 2018) | Slides |

Exercise 9 (November 16, 2018) | Slides |

Exercise 11 (November 30, 2018) | Slides |

Exercise 12 (December 7, 2018) | Slides, Slides |

Exercise 13 (December 14, 2018) | Slides, Slides |

Your grade for the course will be based solely on the written final exam. The exam will cover **all material discussed during the lectures and the exercise classes**.

Some old exams can be found here on the homepage of Group 3, but students are highly discouraged from preparing from the old exams only. It will not be enough to ensure a passing grade.

For questions before the exam, please use the semester break Präsenz.

During the second and the third week of the semester after the exam, you have the possibility to look at your exam during the regular Präsenz hours.

**Probability Essentials**by Jean Jacod and Philip Protter (Springer, 2003)**Stochastic Finance: An Introduction in Discrete Time**by Hans Föllmer and Alexander Schied (Walter de Gruyter, 2011).**Introduction to Stochastic Calculus Applied to Finance**by Damien Lamberton and Bernard Lapeyre (Chapman-Hall, 2008)

For computational aspects, you can consult for example the following books:

**Finanzderivate mit MATLAB**by Michael Günther and Ansgar Jüngel (Vieweg+Teubner, 2010)**The Concepts and Practice of Mathematical Finance**by Mark Joshi (Cambridge University Press, 2008)**Tools for Computational Finance**by Rüdiger Seydel (Springer, 2009)**Binomial Models in Finance**by John van der Hoek and Robert J. Elliott (Springer, 2006)