Numerical methods for mathematical finance (seminar course) (2014/2015)

Course code
Name of lecturer
Leonard Peter Bos
Leonard Peter Bos
Number of ECTS credits allocated
Academic sector
Language of instruction
II sem. dal Mar 2, 2015 al Jun 12, 2015.

Lesson timetable

II sem.
Day Time Type Place Note
Friday 1:30 PM - 4:30 PM lesson Lecture Hall M  

Learning outcomes

In this course we will study basic numerical methods for option pricing.


Binary Trees
- riskless portfolio
- risk neutral probability
- calibrating the tree
Continuous Time
- Geometric Brownian Motion
- the Black-Scholes PDE
- Feynman-Kac and risk-neutrality
Estimating the Volatility from historical data
Acceleration of the backfolding of the tree using the FFT
Other fast(er) methods for trees
Path Dependent Options using a Tree
- Lookback Puts and Calls
- the Cheuk-Vorst algorithm
- American Lookback options
Numerical Methods for Advection-Diffusion Equations
- Euler Explicit
- Euler Implicit
- Crank-Nicholson
- application to the Black-Scholes PDE
Asian Options
- an associated PDE
- eliminating the advection term
American Options
- linear complementary problems
- numerical solution
The Carr-Madan Fourier algorithm (for a call)
Jump Diffusion Models
- compound Poisson processes and their simulation
- the Merton Model
- the Merton formula
- the Carr-Madan algorithm for the Merton Model
- American options under the Merton Model
The fast Gauss Transform and its application to Option Pricing
Calibration using Hisorical Data
- the Schwartz Mean Reverting Model for Comodities
- its calibration using Forward Prices
Monte Carlo Methods
- accelerations
- application to Basket Options
Discretization of SDEs
- Euler discretization
- Milstein discretization

Assessment methods and criteria

The final mark will be bsed on homework assignments as well as a project completed by the student.