Computational Finance and its implementation in Python with applications to option pricing, Green finance and Climate risk
Lecturer: Dr. Andrea Mazzon
Dr. Andrea Mazzon
Dates and Times:
The course takes place after the end of the WS 2021/22.
It consists of 28 academic hours.
Dates and times will be decided with a Doodle poll.
|Final Exam||The date will be decided with a Doodle poll.|
Registration is mandatory. For registration send an email to
including your name and student id (Matrikelnummer) until the 22th of February 2022. Further information will be provided per e-mail.
- Binomial model for option pricing:
- replicating portfolio
- 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.
- Numerical methods for the pricing of green bonds.
- 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
For who is this course?
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 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.