Computational Finance and its implementation in Python applications to option pricing, Green finance and Climate risk
Dr. Andrea Mazzon
Schedule and Venue
| Events | Date/Time | Room |
|---|---|---|
| Lectures Dr. Andrea Mazzon |
| |
| Final Exam | The date will be decided with a Doodle poll. |
Please register for the lecture via mail to mazzon@math.lmu.de until the 10th of February 2023 if you want to take part to the poll deciding the dates. Your email must include name and student id (Matrikelnummer) and have subject "Registration Computational Finance and its implementation in Python". Please note that registration is mandatory.
The course will be given in hybrid mode: both in presence (in the Quantlab) and from remote (in Zoom). Further information will be provided per e-mail.
The aim of the lecture is to connect theory and practice in Mathematical Finance, with applications to option prices, Green finance and Climate risk by coding in Python. We will look at several examples/models and produce some code for each topic, implementing standard and more advanced financial models and the associated numerical procedures.
In particular, here is a tentative schedule.
- Binomial model for option pricing:
- replicating portfolio
- calibration
- different techniques for the evaluation of American options
- convergence, computational efficiency and control variates
- Review of the Monte-Carlo method for the simulation of stochastic processes and option pricing:
- variance reduction techniques: control variate, importance sampling, antithetic variables
- Finite difference methods for the approximation of the solution of PDEs for option pricing:
- Forward Euler, backward Euler, Crank - Nicholson and theta-method: consistency, convergence, stability. Theory and examples.
- Option pricing by Feyman-Kac formula.
- Feynman Kaç formula testing: comparison between the price approximation obtained by solving the PDE and the one got by Monte-Carlo simulation.
- The pricing of Barrier options: comparison between binomial model, Monte-Carlo simulation and Feynman Kaç formula.
- Numerical methods for the valuation of Climate risk and solution of Climate risk-related optimization problems.
- Monte Carlo Methods in Financial Engineering, Paul Glasserman, Springer-Verlag New York, 2004.
- Numerical Solutions of Stochastic Differential Equations, Peter E. Kloeden and Eckhard Platen, Springer-Verlag Berlin Heidelberg, 1992.
- R. Cont and P. Tankov: "Financial Modelling with Jump Processes" Chapman & Hall 2004,
- J. Kienitz, D. Wetterau: "Financial Modelling: Theory, Implementation and Practice with MATLAB Source", Wiley, 2012
- C. Fries : "Mathematical Finance: Theory, Modeling, Implementation". Wiley, 2007.
- M.Gilli, D. Maringer, E. Schumann. "Numerical Methods and Optimization in Finance", Elsevier 2011
Target Participants: Students of the Master in Mathematics or in Financial and Insurance Mathematics.
Pre-requisites: Students are supposed to be familiar with stochastic calculus and pricing theory. Good programming skills and a fair knowledge of Python are also required.
Applicable credits: 3 ECTS. Students may apply the credits from this course to:
- the Master in Financial and Insurance Mathematics, PO 2011 (WP20, WP22, WP23)
- the Master in Financial and Insurance Mathematics, PO 2019 (WP17)
- the Master in Financial and Insurance Mathematics, PO 2021 (WP16, WP27)
- the Master in Mathematics (WP44.3, WP45.2 or WP45.3)
There will be some theoretical as well as some programming exercises, to be solved and run in Python.
In order to succesfully pass the exam, students are required to present and discuss the solution of at least two of the three problems that will be given. During the presentation, some related questions touching the program of the course may be asked.