# Computational Finance with Matlab

## Dr. Alessandro Gnoatto

## Schedule and Venue

LecturesDr. Alessandro Gnoatto |
28.07.2014 - 01.08.2014 from 9:00 - 13:00 / 14:00 - 18:00. | quantLabRoom B 121 |

Exercises |
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Final Written Exam |
25.08.2014 at 14.00 - Written Exam 120 min. |

## Course Description

**Content:**The aim of the lecture is to connect theory and practice in Mathematical Finance. We will look at several examples/models and will produce Matlab/GNU Octave code for each topic allowing us to implement standard and advanced financial models and the associated numerical procedures.

**Schedule of the lecture:**

- Introduction to Matlab.
- Option pricing using binomial trees.
- The Black-Scholes model: closed form solution, Greeks, Monte Carlo simulation, , implied volatility via bisection and Newton-Raphson algorithms.
- Monte Carlo in a Black-Scholes setting: pricing of Asian, Look-back and Barrier options. Estimating Greeks using Monte Carlo.
- Transform methods in Finance: revisiting the Black Scholes model in a FFT framework. The Carr and Madan Formula and the Lewis approach.
- Stochastic volatility: the Heston model. Monte Carlo for stochastic volatility models – the Milstein scheme. FFT for the Heston model.

## References

- Matlab primer: http://www.math.toronto.edu/mpugh/primer.pdf.
- Matlab and GNU Octave are very similar, however, here you can find a list with some differences: http://en.wikibooks.org/wiki/MATLAB_Programming/Differences_between_Octave_and_MATLAB

## For whom is this course?

**Target Participants:** Master students of Business Mathematics.

**Pre-requisites: ** A strong command of measure-theoretic probability and stochastic calculus is assumed. It is assumed that the students attended the lecture Finanzmathematik II.

**Applicable credits: ** Students may apply the credits from this course to Masterprüfungen Wirtschaftsmathematik (WP61).

## Exercises

Correcting your answers and thinking through the exercises is the best preparation for the exam. The solutions need not be submitted, but if you wish them to be corrected, please submit your exercise solutions.

**Exercise Handouts:** Problem sheets and Solutions will be uploaded here during the course.