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

Dr. Lorenzo Torricelli


Schedule and Venue

Lectures and Exercises
Dr. Lorenzo Torricelli

19.02.2018 - 24.02.2018

h. 9.00-13.00 and 14.00-18.00


quantLab
Room B 121

Final Exam

26.02.2018 h. 10.00: Projects handout

5.03.2018 h. 10.00: Projects presentation (exam  day)

  


Course Description

  • 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.


References

  1. J. Gatheral, "The volatility surface: A practitioner's guide", Wiley 2006
  2. R. Cont and P. Tankov: "Financial Modelling with Jump Processes" Chapman & Hall 2004,
  3. J. Kienitz, D. Wetterau: "Financial Modelling: Theory, Implementation and Practice with MATLAB Source", Wiley, 2012
  4. C. Fries : "Mathematical Finance: Theory, Modeling, Implementation". Wiley, 2007.
  5. M.Gilli, D. Maringer, E. Schumann. "Numerical Methods and Optimization in Finance", Elsevier 2011
The following Matlab and GNU Octave tutorials can be useful:
  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

For whom is this course?

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).


Exercises and Handouts

Lecture notes with the course material and Exercises to be carried out during the lecture will be distributed.


Final Exam

The exam will consist of a discussion of a project which will be assigned to you at the end of the course, consisting on producing a MATLAB/Octave implementation on a topic inherent to those discussed during the course. You will have to work in groups of two people (one group of three in case of an odd number) to each of which a different problem is assigned.