Computational finance and its implementation in Octave/Matlab with applications to equity modelling

• Content:

  The aim of the lecture is to connect theory and practice in Mathematical Finance, with a focus on equity models. We will look at several examples/models and will produce Matlab/GNU Octave code for each topic allowing us to implement standard and more advanced financial models and the associated numerical procedures. The lectures will be held in an interactive format alternating theory, code illustration/demonstrations, and implementation exercises to be carried out during the class.

• Topics:

1. The Black-Scholes implied volatility: bisection and Newton-Raphson algorithms. The volatility surface and local volatility.
2. Monte Carlo methods for stochastic volatility, Jump diffusion and Lévy models;
3. Transform methods in Finance: the Heston, Carr-Madan and the Lewis approach;
4. Greeks and Hedging: finite differences and Monte-Carlo simulation, Delta/Gamma and mean variance hedging;
5. Exotic derivatives: PDE in the Black-Scholes and stochstic volatility models, binomial trees for American options;

The topics and the content of the course can be subject to revision or partial modification in due course.

Perspective participants are kindly invited to send an email at torricel@math.lmu.de mentioning their interest.

1. Matlab primer: http://www.math.toronto.edu/mpugh/primer.pdf.
2. 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

Target Participants: Master students of Financial Mathematics and Mathematics.

Pre-requisites:   Probability theory, Stochastic calculus, Black-Scholes, basic Complex analysis and general option pricing theory. Some prior knowledge of the commonly used numerical analysis methods used in finance is helpful. Some basic knowledge of Matlab/Octave is also beneficial, but we will try to keep the requisite to a minimum. Minimal notion of Fourier analysis are adavntegeous, but not a requirement.

Applicable credits:  6 ECTS. Students may apply the credits from this course to the Masters in Financial Mathematics (WP61) or Master in Mathematics (ideally WP42 or WP46, but other possibilities can be dicussed).