Josef Teichmann: Catalogue data in Autumn Semester 2016
|Name||Prof. Dr. Josef Teichmann|
Professur für Finanzmathematik
ETH Zürich, HG G 54.2
|Telephone||+41 44 632 31 74|
|401-0613-00L||Probability and Statistics||6 credits||3V + 2U||J. Teichmann|
|Abstract||Basic concepts from probability and statistics:|
- introduction to probability theory
- short introduction to basic concepts and methods from statistics
|Objective||a) ability to understand the covered methods from probability theory and to apply them in other contexts|
b) probabilistic thinking and stochastic modelling
c) ability to perform basic statistical tests and to interpret the results
|Content||Basic concepts from probability and statistics with special emphasis on the topics needed in computer science|
The conceptual goals are
- the laws of randomness and probabilistic thinking (thinking in probabilities)
- understanding and intuition for stochastic modelling
- simple and basic methods from statistics
The contents of the course encompasses
- an introduction to probability theory: basic concepts (probability space, probability measure), independence, random variables, discrete and continuous distributions, conditional probability, expectation and variance, limit theorems
- methods from statistics: parameter estimation, maximum likelihood and moment methods, tests, confidence intervals
|Lecture notes||Lecture notes for the course (in German) will be made available electronically at the beginning of the course.|
|401-4611-66L||Rough Path Theory and Regularity Structures||6 credits||3V||J. Teichmann, D. Prömel|
|Abstract||The course provides an introduction to the theory of controlled rough paths with focus on stochastic differential equations. In parallel, Martin Hairer's new theory of regularity structures is introduced taking controlled rough paths as guiding examples. In particular, the course demonstrates how to use the theory of regularity structures to solve singular stochastic PDEs.|
|Objective||The main goal is to develop simultaneously the basic concepts of rough path theory and Hairer's regularity structures.|
|Literature||- Peter Friz and Martin Hairer, A Course on Rough Paths: With an Introduction to|
Regularity Structures, Springer, 2014.
- Martin Hairer, Introduction to regularity structures, Braz. J. Probab. Stat. 29 (2015),
no. 2, 175-210.
- Peter Friz and Nicolas Victoir, Multidimensional stochastic processes as rough paths.
Theory and applications, Cambridge University Press, 2010.
- Martin Hairer, A theory of regularity structures, Inventiones mathematicae (2014), 1-236.
- Ajay Chandra and Hendrik Weber, Stochastic PDEs, Regularity Structures, and Inter-
acting Particle Systems, Preprint arXiv:1508.03616.
|Prerequisites / Notice||Requirements: Brownian Motion and Stochastic Calculus|
|401-5820-00L||Seminar in Computational Finance for CSE||4 credits||2S||J. Teichmann|
|Content||We aim to comprehend recent and exciting research on the nature of|
stochastic volatility: an extensive econometric research  lead to new in-
sights on stochastic volatility, in particular that very rough fractional pro-
cesses of Hurst index about 0.1 actually provide very attractive models. Also
from the point of view of pricing  and microfoundations  these models
are very convincing.
More precisely each student is expected to work on one specified task
consisting of a theoretical part and an implementation with financial data,
whose results should be presented in a 45 minutes presentation.
|Literature|| C. Bayer, P. Friz, and J. Gatheral. Pricing under rough volatility.|
Quantitative Finance , 16(6):887-904, 2016.
 F. M. Euch, Omar El and M. Rosenbaum. The microstructural founda-
tions of leverage effect and rough volatility. arXiv:1609.05177 , 2016.
 O. E. Euch and M. Rosenbaum. The characteristic function of rough
Heston models. arXiv:1609.02108 , 2016.
 J. Gatheral, T. Jaisson, and M. Rosenbaum. Volatility is rough.
arXiv:1410.3394 , 2014.
|Prerequisites / Notice||Requirements: sound understanding of stochastic concepts and of con-|
cepts of mathematical Finance, ability to implement econometric or simula-
tion routines in MATLAB.
|401-5910-00L||Talks in Financial and Insurance Mathematics||0 credits||1K||P. Cheridito, M. Schweizer, M. Soner, J. Teichmann, M. V. Wüthrich|
|Content||Regular research talks on various topics in mathematical finance and actuarial mathematics|