- Alternative course title
- Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods
- Lecturer
- Kristin Kirchner
- Coordinator
- Diyora Salimova
- Assistants
- Bryn Davies, Martin Stefanik

- Monday 15:15-17:00, HG D 1.2
- Wednesday 13:15-14:00, HG E 1.1

A closed-book, computer-based exam will take place

**date:**December 18, 2019**time:**13:00 until 15:00 (students must arrive before 12:50)**place:**HG E 19**duration:**120 minutes

There will be weekly homework assignments, which are due in the break between the two hours of lecture on Monday, i.e. at 16:15.

Solutions to the theoretical questions can be handed in in the lecture room in paper or scanned and submitted via e-mail before the deadline. Code must be handed in online using the submission interface. Only in case the submission does not work: send your codes via E-Mail to your assistant and contact Diyora Salimova to update the configuration of the submission interface.

Submissions of problem sheets in a group are not allowed.

Each problem will be marked according to the following scheme:

- 0 - no submission
- 0.5 - incomplete or insufficient submission
- 1 - sufficient submission.

MUST take the written exam at the end of the semester. Students who acquire at least 70% of the points attainable by doing the weekly problem sheets, i.e., in average 0.7 points per exercise, are given an additive bonus of 0.25 on their final grade (e.g. grade 4.5 (without bonus) will be grade 4.75 (with bonus)).

(i.e. only require a "pass" grade, which includes D-MATH PhD students at ETH) must achieve at least 70% of the maximal number of points attainable by sufficient submission of the weekly homework problem sheets, i.e. in average 0.7 points must be achieved per problem. Students who did not achieve the required percentage of points in the weekly homework problem sheets can still achieve a "pass" by taking the final written exam.

exercise sheet | due by | code templates | solutions |
---|---|---|---|

Exercise sheet 1 | September 30 | no templates | Solution 1 |

Exercise sheet 2 | October 7 | no templates | Solution 2 |

Exercise sheet 3 | October 14 | Templates sheet 3 | Solution 3 |

Exercise sheet 4 | October 21 | no templates | Solution 4 |

Exercise sheet 5 | October 28 | no templates | Solution 5 |

Exercise sheet 6 | November 4 | no templates | Solution 6 |

Exercise sheet 7 | November 11 | no templates | Solution 7 |

Exercise sheet 8 | November 18 | no templates | Solution 8 |

Exercise sheet 9 | November 25 | EulerMaruyama.m | Solution 9 |

Exercise sheet 10 | December 2 | Templates sheet 10 | Solution 10 |

Exercise sheet 11 | December 9 | no templates | Solution 11 |

time | room | assistant |
---|---|---|

Wed 14:15-15:00 | HG D 7.1 | Martin Stefanik (martin.stefanik@math.ethz.ch) |

Wed 14:15-15:00 | HG E 1.1 | Bryn Davies (bryn.davies@sam.math.ethz.ch) |

Monday, 17:15 until 18:00 at the table at HG G 53.

The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.

- Probability and measure theory.
- Basic numerical analysis.
- Basics of MATLAB programming.

- Generation of random numbers.
- Monte Carlo methods for the numerical integration of random variables.
- Stochastic processes and Brownian motion.
- Stochastic ordinary differential equations (SODEs).
- Numerical approximations of SODEs.
- Applications to computational finance: Option valuation.

Students of ETH can download Matlab via Stud-IDES for free (product name 'Matlab free')

- P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004.
- P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992.