Fall Semester 2016

Stochastic Methods + Lab


This course is a first hands-on introduction to stochastic modeling. Examples will mostly come from the area of Financial Mathematics, so that this course plays a central role in the education of students interested in Quantitative Finance and Mathematical Economics.

Topics include binomial tree models, discrete Brownian paths, stochastic ODEs, Monte-Carlo methods, finite differences solutions for the Black-Scholes equation, and an introduction to time series analysis, parameter estimation, and calibration. Students will program and explore all basic techniques in a numerical programming environment and apply these algorithms to real data whenever possible.

Contact Information:
Instructor:Marcel Oliver
Office hours:   We/Th 10:00 in Research I, 107
TA:Kim Philipp Jablonski

Time and Place:
Tu 8:15-11:00 in East Hall 4
Th 11:15-13:30 in East Hall 4

The class grade is based on individually graded exercises. These are either worked on during lab sessions or as take-home work to be turned in up to one week later. The final task sheet will a larger project worth 20% of the grade.

Submission of Work:


Scientific Python Resources:

Course Schedule (subject to change!)

01/09/2016: Introduction to Scientific Python
06/09/2016: Basic notions from finance (present value, forward value, annuities, amortization schedule, yields, internal rate of return); Basic computational tools (vectorized formulation of problems, timing issues, root finding methods).
Lyuu, Sections 3.1-3.4
08/09/2016: Introduction to git
13/09/2016: Bonds, zero coupon bonds, level coupon bonds
Lyuu, Section 3.5
15/09/2016: Immunization, Macaulay duration, immunization (begin)
Lyuu, Sections 4.1-4.2
20/09/2016: Immunization (ctd.), convexity (brief); The term structure of interest rates
Lyuu, Sections 4.2-5.2
22/09/2016: No class
27/09/2016: Options: introduction, single-period model, risk-neutral probabilites, binomial tree mathod (start)
29/09/2016: Binomial tree method (implementation)
04/10/2016: Binomial tree method: scaling and calibration
06/10/2016: Binomial tree method: visualization, convergenc; call-put parity
11/10/2016: Central limit theorem for binomial distributions; derivation of the Black-Scholes formula
13/10/2016: Brownian motion
18/10/2016: Stochastic integrals
20/10/2016: Stochastic differential equations, Euler-Maruyama method
27/10/2016: Weak and strong convergence
01/11/2016: Ito Lemma
03/11/2016: Derivation of the Black-Scholes equation; finite differences
10/11/2016: Stability; explicit vs. implicit timestepping, tridiagonal systems

Last modified: 2016/09/04
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2016/acm221/index.html
Marcel Oliver (m.oliver@jacobs-university.de)