Search result: Catalogue data in Spring Semester 2018
Quantitative Finance Master see Link Students in the Joint Degree Master's Programme "Quantitative Finance" must book UZH modules directly at the UZH. Those modules are not listed here. | ||||||
Core Courses | ||||||
Economic Theory for Finance No course offerings in this semester | ||||||
Mathematical Methods for Finance | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
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401-4658-00L | Computational Methods for Quantitative Finance: PDE Methods | W | 6 credits | 3V + 1U | C. Schwab | |
Abstract | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB programming and knowledge of numerical mathematics at ETH BSc level. | |||||
Objective | Introduce the main methods for efficient numerical valuation of derivative contracts in a Black Scholes as well as in incomplete markets due Levy processes or due to stochastic volatility models. Develop implementation of pricing methods in MATLAB. Finite-Difference/ Finite Element based methods for the solution of the pricing integrodifferential equation. | |||||
Content | 1. Review of option pricing. Wiener and Levy price process models. Deterministic, local and stochastic volatility models. 2. Finite Difference Methods for option pricing. Relation to bi- and multinomial trees. European contracts. 3. Finite Difference methods for Asian, American and Barrier type contracts. 4. Finite element methods for European and American style contracts. 5. Pricing under local and stochastic volatility in Black-Scholes Markets. 6. Finite Element Methods for option pricing under Levy processes. Treatment of integrodifferential operators. 7. Stochastic volatility models for Levy processes. 8. Techniques for multidimensional problems. Baskets in a Black-Scholes setting and stochastic volatility models in Black Scholes and Levy markets. 9. Introduction to sparse grid option pricing techniques. | |||||
Lecture notes | There will be english, typed lecture notes as well as MATLAB software for registered participants in the course. | |||||
Literature | R. Cont and P. Tankov : Financial Modelling with Jump Processes, Chapman and Hall Publ. 2004. Y. Achdou and O. Pironneau : Computational Methods for Option Pricing, SIAM Frontiers in Applied Mathematics, SIAM Publishers, Philadelphia 2005. D. Lamberton and B. Lapeyre : Introduction to stochastic calculus Applied to Finance (second edition), Chapman & Hall/CRC Financial Mathematics Series, Taylor & Francis Publ. Boca Raton, London, New York 2008. J.-P. Fouque, G. Papanicolaou and K.-R. Sircar : Derivatives in financial markets with stochastic volatility, Cambridge Univeristy Press, Cambridge, 2000. N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. | |||||
Prerequisites / Notice | Start of the lecture: WED, 28 Feb. 2018 (second week of the semester). | |||||
401-3629-00L | Quantitative Risk Management | W | 4 credits | 2V | P. Cheridito | |
Abstract | This course introduces methods from probability theory and statistics that can be used to model financial risks. Topics addressed include loss distributions, risk measures, extreme value theory, multivariate models, copulas and dependence structures as well as operational risk. | |||||
Objective | The goal is to learn the most important methods from probability theory and statistics used in financial risk modeling. | |||||
Content | 1. Introduction 2. Basic Concepts in Risk Management 3. Empirical Properties of Financial Data 4. Financial Time Series 5. Extreme Value Theory 6. Multivariate Models 7. Copulas and Dependence 8. Operational Risk | |||||
Lecture notes | Course material is available on Link | |||||
Literature | Quantitative Risk Management: Concepts, Techniques and Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2015 (Revised Edition) Link | |||||
Prerequisites / Notice | The course corresponds to the Risk Management requirement for the SAA ("Aktuar SAV Ausbildung") as well as for the Master of Science UZH-ETH in Quantitative Finance. | |||||
Elective Courses | ||||||
Economic Theory for Finance | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
401-3956-00L | Economic Theory of Financial Markets Does not take place this semester. | W | 4 credits | 2V | M. V. Wüthrich | |
Abstract | This lecture provides an introduction to the economic theory of financial markets. It presents the basic financial and economic concepts to insurance mathematicians and actuaries. | |||||
Objective | This lecture aims at providing the fundamental financial and economic concepts to insurance mathematicians and actuaries. It focuses on portfolio theory, cash flow valuation and deflator techniques. | |||||
Content | We treat the following topics: - Fundamental concepts in economics - Portfolio theory - Mean variance analysis, capital asset pricing model - Arbitrage pricing theory - Cash flow theory - Valuation principles - Stochastic discounting, deflator techniques - Interest rate modeling - Utility theory | |||||
Prerequisites / Notice | The exams ONLY take place during the official ETH examination period. This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under Link. Knowledge in probability theory, stochastic processes and statistics is assumed. | |||||
Mathematical Methods for Finance | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
401-3936-00L | Data Analytics for Non-Life Insurance Pricing | W | 4 credits | 2V | C. M. Buser, M. V. Wüthrich | |
Abstract | We study statistical methods in supervised learning for non-life insurance pricing such as generalized linear models, generalized additive models, Bayesian models, neural networks, classification and regression trees, random forests, gradient boosting machines and support vector machines. Moreover, we present unsupervised learning methods applied to telematics car driving data. | |||||
Objective | The student is familiar with classical actuarial pricing methods as well as with modern machine learning methods for insurance pricing and prediction. | |||||
Content | We present the following chapters: - generalized linear models (GLMs) - generalized additive models (GAMs) - credibility theory - classification and regression trees (CARTs) - bagging, random forests and boosting - support vector machines (SVMs) - unsupervised learning methods - telematics car driving data | |||||
Lecture notes | The lecture notes are available from: Link | |||||
Prerequisites / Notice | This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under Link Good knowledge in probability theory, stochastic processes and statistics is assumed. | |||||
401-4920-00L | Market-Consistent Actuarial Valuation | W | 4 credits | 2V | M. V. Wüthrich, H. Furrer | |
Abstract | Introduction to market-consistent actuarial valuation. Topics: Stochastic discounting, full balance sheet approach, valuation portfolio in life and non-life insurance, technical and financial risks, risk management for insurance companies. | |||||
Objective | Goal is to give the basic mathematical tools for describing insurance products within a financial market and economic environment and provide the basics of solvency considerations. | |||||
Content | In this lecture we give a full balance sheet approach to the task of actuarial valuation of an insurance company. Therefore we introduce a multidimensional valuation portfolio (VaPo) on the liability side of the balance sheet. The basis of this multidimensional VaPo is a set of financial instruments. This approach makes the liability side of the balance sheet directly comparable to its asset side. The lecture is based on four sections: 1) Stochastic discounting 2) Construction of a multidimensional Valuation Portfolio for life insurance products (with guarantees) 3) Construction of a multidimensional Valuation Portfolio for a run-off portfolio of a non-life insurance company 4) Measuring financial risks in a full balance sheet approach (ALM risks) | |||||
Literature | Market-Consistent Actuarial Valuation, 2nd edition. Wüthrich, M.V., Bühlmann, H., Furrer, H. EAA Series Textbook, Springer, 2010. ISBN: 978-3-642-14851-4 Wüthrich, M.V., Merz, M. Claims Run-Off Uncertainty: The Full Picture SSRN Manuscript ID 2524352 (2015). Wüthrich, M.V., Embrechts, P., Tsanakas, A. Risk margin for a non-life insurance run-off. Statistics & Risk Modeling 28 (2011), no. 4, 299--317. Financial Modeling, Actuarial Valuation and Solvency in Insurance. Wüthrich, M.V., Merz, M. Springer Finance 2013. ISBN: 978-3-642-31391-2 | |||||
Prerequisites / Notice | The exams ONLY take place during the official ETH examination period. This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under Link. Knowledge in probability theory, stochastic processes and statistics is assumed. | |||||
401-3642-00L | Brownian Motion and Stochastic Calculus | W | 10 credits | 4V + 1U | W. Werner | |
Abstract | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | |||||
Objective | This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations. | |||||
Lecture notes | Lecture notes will be distributed in class. | |||||
Literature | - J.-F. Le Gall, Brownian Motion, Martingales, and Stochastic Calculus, Springer (2016). - I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, Springer (1991). - D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer (2005). - L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, vol. 1 and 2, Cambridge University Press (2000). - D.W. Stroock, S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer (2006). | |||||
Prerequisites / Notice | Familiarity with measure-theoretic probability as in the standard D-MATH course "Probability Theory" will be assumed. Textbook accounts can be found for example in - J. Jacod, P. Protter, Probability Essentials, Springer (2004). - R. Durrett, Probability: Theory and Examples, Cambridge University Press (2010). | |||||
227-0224-00L | Stochastic Systems | W | 4 credits | 2V + 1U | F. Herzog | |
Abstract | Probability. Stochastic processes. Stochastic differential equations. Ito. Kalman filters. St Stochastic optimal control. Applications in financial engineering. | |||||
Objective | Stochastic dynamic systems. Optimal control and filtering of stochastic systems. Examples in technology and finance. | |||||
Content | - Stochastic processes - Stochastic calculus (Ito) - Stochastic differential equations - Discrete time stochastic difference equations - Stochastic processes AR, MA, ARMA, ARMAX, GARCH - Kalman filter - Stochastic optimal control - Applications in finance and engineering | |||||
Lecture notes | H. P. Geering et al., Stochastic Systems, Measurement and Control Laboratory, 2007 and handouts | |||||
401-3917-00L | Stochastic Loss Reserving Methods | W | 4 credits | 2V | R. Dahms | |
Abstract | Loss Reserving is one of the central topics in non-life insurance. Mathematicians and actuaries need to estimate adequate reserves for liabilities caused by claims. These claims reserves have influence all financial statements, future premiums and solvency margins. We present the stochastics behind various methods that are used in practice to calculate those loss reserves. | |||||
Objective | Our goal is to present the stochastics behind various methods that are used in prctice to estimate claim reserves. These methods enable us to set adequate reserves for liabilities caused by claims and to determine prediction errors of these predictions. | |||||
Content | We will present the following stochastic claims reserving methods/models: - Stochastic Chain-Ladder Method - Bayesian Methods, Bornhuetter-Ferguson Method, Credibility Methods - Distributional Models - Linear Stochastic Reserving Models, with and without inflation - Bootstrap Methods - Claims Development Result (solvency view) - Coupling of portfolios | |||||
Literature | M. V. Wüthrich, M. Merz, Stochastic Claims Reserving Methods in Insurance, Wiley 2008. | |||||
Prerequisites / Notice | The exams ONLY take place during the official ETH examination periods. This course will be held in English and counts towards the diploma "Aktuar SAV". For the latter, see details under Link. Basic knowledge in probability theory is assumed, in particular conditional expectations. | |||||
Master's Thesis see Link |
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