Search result: Catalogue data in Spring Semester 2013
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 | A. Barth | |
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 | The 2009 title of this course unit was "Computational Methods for Quantitative Finance II: Finite Element and Finite Difference Methods". | |||||
401-3629-00L | Quantitative Risk Management | W | 4 credits | 2V | P. Embrechts | |
Abstract | The aim of this course is to present a concise overview of mathematical methods from the areas of probability and statistics that can be used by financial institutions to model market, credit and operational risk. Topics addressed include loss distributions, multivariate models, dependence and copulas, extreme value theory, risk measures, risk aggregation and risk allocation. | |||||
Objective | The aim of this course is to present a concise overview of mathematical methods from the areas of probability and statistics that can be used by financial institutions to model market, credit and operational risk. | |||||
Content | 1. Risk in Perspective 2. Basic Concepts 3. Multivariate Models 4. Copulas and Dependence 5. Aggregate Risk 6. Extreme Value Theory 7. Operational Risk and Insurance Analytics | |||||
Lecture notes | Quantitative Risk Management: Concepts, Techniques, Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2005 | |||||
Literature | Quantitative Risk Management: Concepts, Techniques, Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2005, and references therein. | |||||
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 | W | 4 credits | 2V | M. V. Wüthrich | |
Abstract | This lectures provides an introduction to economic theory of financial markets. It aims to provide a grounding in fundamental financial concepts to insurance mathematicians and actuaries. | |||||
Objective | This lecture aims to provide a grounding in fundamental financial concepts to insurance mathematicians and actuaries. The main focus is to give an actuarial education and training in portfolio theory, cash flow theory and deflator techniques. | |||||
Content | We treat the following topics: - Fundamental concepts in economics - Portfolio theory - Mean variance analysis, CAPM - Arbitrage pricing theory - Cash flow theory - Valuation principles - Stochastic discounting, deflator techniques - Interest rate modeling - Utility theory | |||||
Prerequisites / Notice | 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 | |
401-4920-00L | Market-Consistent Actuarial Valuation Does not take place this semester. | W | 4 credits | 2V | M. V. Wüthrich | |
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 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 minimal 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) | |||||
Lecture notes | Market-Consistent Actuarial Valuation, 2nd edition. Wüthrich, Mario V., Bühlmann, Hans, Furrer, Hansjörg EAA Series Textbook, Springer, 2010. ISBN: 978-3-642-14851-4 M.V. Wüthrich, P. Embrechts and A. Tsanakas. Risk margin for a non-life insurance run-off. Statistics & Risk Modeling 28 (2011), no. 4, 299--317. | |||||
Literature | Market-Consistent Actuarial Valuation, 2nd edition. Wüthrich, Mario V., Bühlmann, Hans, Furrer, Hansjörg EAA Series Textbook, Springer, 2010. ISBN: 978-3-642-14851-4 M.V. Wüthrich, P. Embrechts and A. Tsanakas. Risk margin for a non-life insurance run-off. Statistics & Risk Modeling 28 (2011), no. 4, 299--317. | |||||
Prerequisites / Notice | 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 | A.‑S. Sznitman | |
Abstract | Stochastic analysis is an important tool in the study of stochastic processes. The lecture will cover some basic objects of stochastic analysis. The following topics will for instance be discussed: Brownian motion: construction and properties, stochastic integration, Ito's formula and applications,stochastic differential equations and their links to partial differential equations. | |||||
Objective | Brownian motion: construction and properties, stochastic integration, Ito's formula and applications, stochastic differential equations and their links to partial differential equations. | |||||
Content | Stochastic analysis is an important tool in the study of stochastic processes. The lecture will cover some basic objects of stochastic analysis. The following topics will for instance be discussed: Brownian motion: construction and properties, stochastic integration, Ito's formula and applications,stochastic differential equations and their links to partial differential equations. | |||||
Literature | DURRETT, R.:"Brownian motion and martingales in analysis", Wadsworth, Belmont, 1984. IKEDA, N.- WATANABE, S.: "Stochastic Differential Equations and Diffusion Processes", second edition, North Holland, Amsterdam, 1979. KARATZAS, I.- SHREVE, S.:"Brownian motion and stochastic calculus", Springer, Berlin, 1988. REVUZ, D.- YOR, M.:"Continuous Martingales and Brownian Motion", Springer, Berlin, 1991. ROGERS, L.C.G.- WILLIAMS, D. :"Diffusions, Markov Processes, and Martingales", vol. 1 and 2, Wiley, Chichester, 1987, 1994. STROOCK,D.W.:"Lectures on Stochastic Analysis: Diffusion Theory", London Mathematical Society Student Texts 6, Cambridge University Press, 1987. STROOCK,D.W.- VARADHAN, S.R.S.: "Multidimensional Diffusion Processes", Springer, Berlin, 1979. | |||||
Prerequisites / Notice | This course replaces the former course 401-3642-00L Stochastic Processes and Stochastic Analysis. Moreover it has a large overlap with the course 401-4608-10L Brownian Motion and Stochastic Calculus from FS 2010. Therefore it is forbidden to register for an examination for more than one of the three courses mentioned. | |||||
401-3928-00L | Reinsurance Analytics | W | 4 credits | 2V | P. Antal | |
Abstract | History and motivation. Basic Risk Theory applied to reinsurance. The reinsurance market and lines of business. Pricing reinsurance contracts. Solvency and capital considerations. Alternative Risk Transfer. | |||||
Objective | Understanding the economic value creation through reinsurance. Knowing the most common types of reinsurance and being able to represent the reinsured losses in terms of random variables. Understanding the economic and mathematic principles underlying the premium calculations for reinsurance contracts. | |||||
Content | History of reinsurance. Historic examples of large events. Fundamentals of reinsurance & contract types. Overview of large reinsurance companies & market places. Lines of business explained: Property, Casualty, Life & Health, Credit & Surety. Risk theoretical principles including frequency/severity models, stop-loss transforms and exposure curves. Exposure and experience rating. Capital impact of reinsurance: Swiss Solvency Test and Solvency 2, rating agency view, insurance vs. investment risks. Insurance Linked Securities: cat bonds, industry loss warranties. | |||||
Lecture notes | A script will be made available in electronic form. | |||||
Prerequisites / Notice | Former course title: "Insurance Analytics" | |||||
401-3919-60L | An Introduction to the Modelling of Extremes | W | 4 credits | 2V | P. Embrechts | |
Abstract | This course yields an introduction into the one-dimensional theory of extremes, and this both from a probabilistic as well as statistical point of view. This course can be seen as a first course on extremes, a sequel concentrating more on multivariate extremes. | |||||
Objective | In this course, students learn to distinguish between so-called normal models, i.e. models based on the normal or Gaussian distribution, and so-called heavy-tailed or power-tail models. They learn to do some standard modelling and data analysis for one-dimensional data. The probabilistic key theorems are the Fisher-Tipett Theorem and the Balkema-de Haan-Pickands Theorem. These lead to the statistical techniques for the analysis of extremes or rare events known as the Block Method, and Peaks Over Threshold method, respectively. | |||||
Content | - Introduction to rare or extreme events - Regular Variation - The Convergence to Types Theorem - The Fisher-Tippett Theorem - The Method of Block Maxima - The Maximal Domain of Attraction - The Fre'chet, Gumbel and Weibull distributions - The POT method - The Point Process Method: a first introduction - The Pickands-Balkema-de Haan Theorem and its applications - Some extensions and outlook | |||||
Lecture notes | There will be no script available. | |||||
Literature | At a more elementary level: [1] S.G. Coles (2001) An Introduction to Statistical Modeling of Extreme Values. Springer. [2] R.-D. Reiss and M. Thomas (1997) Statistical Analyis of Extreme Values. Birkhaeuser. At an intermediate level: [3] J. Beirlant, Y. Goegebeur, J. Segers and J.L. Teugels (2004) Statistics of Extremes: Theory and Applications, Wiley. [4] P. Embrechts, C. Klueppelberg and T. Mikosch (1997) Modelling Extremal Events for Insurance and Finance. Springer. [5] S. I. Resnick (2007) Heavy-Tail Phenomena. Probabilistic and Statistical Modeling. Springer. At a more advanced level: [6] L. de Haan and A. Ferreira (2006) Extreme Value Theory. An Introduction. Springer. [7] S. I. Resnick (1987) Extreme Values, Regular Variation, and Point Processes. Springer. | |||||
Prerequisites / Notice | The course will be taught by Prof. Natalia Nolde. | |||||
Master Thesis | ||||||
Number | Title | Type | ECTS | Hours | Lecturers | |
401-4990-04L | Master Thesis No enrolment to this course at ETH Zurich. | O | 30 credits | 57D | Professors | |
Abstract | Any field of (mathematical) finance is acceptable, insurance related topics included. | |||||
Objective | We want to be able to appraise your ability 1. to identify and analyse a problem on your own and 2. to apply for that purpose the tools, techniques and concepts you have learned in the courses with little or even no guidance. | |||||
Content | Nature of the Master Thesis You have a lot of flexibility in your choice of project. One possible choice is to write a 'clinical paper' such as those published regularly in the Journal of Financial Economics. A clinical paper is an extended case study, which uses rather more empirical finance techniques than do the more classical, Harvard-type case studies. Another possible choice is to conduct an empirical study on a sample of companies, rather than the single company that is the focus of a clinical paper. Yet another choice is to write a theory paper like those published in Mathematical Finance or Finance and Stochastics. Whatever the choice you make, you should guard against writing a simple survey of the literature. Such surveys do not fulfil the requirements for the Masters thesis. Experience shows that a Master Thesis is in general not ready for publication, because it is (and should be) more detailed than a published paper, on the other hand it needs careful editing and reviewing. Therefore, if you aim for a publication, plan on investing substantial time after handing in your Masters thesis. Role of the supervisor The Master Thesis supervisor has an important, but limited role. He or she is to ensure that the topic you have agreed on is both acceptable and feasible in the limited time, and that the method of analysis you have chosen is appropriate and correct. Once this is done, you are essentially on your own until you hand in the Master Thesis for grading. The thesis supervisor is not expected to read a first draft of the report. However, arrange for meetings with your supervisor to report briefly about your progress so that he/she can give you some suggestions and bring you on the right track again if necessary. Choice of topics Any field of (mathematical) finance is acceptable, insurance related topics included. Examples of possible topics are mergers and acquisitions, distribution policy, financing policy, investment policy, restructuring activity, real options valuation, derivatives pricing, hedging, fixed-income valuation, interest rate contingent claims valuation, credit-sensitive contingent claims valuation, operational risk modelling, model risk issues, securitization, numerical methods for option valuation, time series modelling, capital allocation, performance measurement, risk measurement, and many more. | |||||
Prerequisites / Notice | Finding a supervisor and a topic Any lecturer or professor of the University of Zurich, the ETH Zurich or the MAS Finance program can be your thesis supervisor. If you want to choose any other supervisor (e.g., a professor from another university, a practitioner from the local financial industry, etc.), the supervisor and the topic need the approval of the director of the MAS Finance program. Since we encourage a strong cooperation with the financial industry, consider also the following thoughts: * Your thesis is officially supervised by a local professor, but a practitioner comes up with the precise topic and gives you the needed guidance. * You already have contacts to the financial industry (because you received a tuition fee grant, for example) and you use these contacts to negotiate for an interesting project and guidance. * You are eager to work on a practical project, but you currently lack the industry contacts. In this case, ask one of the lecturers or the director of the MAS Finance program for contact persons. * You might want to combine the Masters thesis with a part-time internship in the financial industry. While this earns you some money to cover your living expenses, it makes it harder to find an arrangement. In any case, make sure your thesis supervisor is really interested in the topic you plan to work on. Suggested length and form The Master Thesis should be about 20 pages long, although you should be aware that it is in fact quality and not quantity that matters. In essence, you should tell us as much as - and no more than - we need to understand what the problem is and what we can learn from it or how you have solved it. Your Master Thesis should be typed and printed in reasonable quality. You should familiarise yourself with the necessary text processing or typesetting software you plan to use before you start to work on your Masters thesis. If you plan on writing a mathematically-orientated thesis (i.e., lots of formulas), the free TeX/LaTeX typesetting software is a good option, but requires a substantial initial time investment. We expect you to write your thesis in English. Exact proofreading is required and use of a spelling checker recommended. Master Thesis in groups The official rules of the MAS Finance program allow groups of two or three persons to write a joint Master Thesis. However, you have to apply in advance for permission and give good reasons. The director of the program will check back with the thesis supervisor and might consult the scientific advisers of the program before permission can be granted. Groups of three persons need really exceptional reasons to get permission. Registration of Master Thesis Please register your Master Thesis as soon as you start it but not later than 1st of July. Use the provided form available in PDF format, which you and your thesis supervisor have to fill in and sign. Everyone is responsible for the part above his/her signature. Send the completed form to Ms. Aline Strolz. The program director will fix the due date and sign, Ms. Strolz will send a copy to you and your thesis supervisor. Deadline The project should start in July or early August after the examinations and has to finish exactly four months later. The thesis supervisor does not have the discretion to grant any extension whatsoever. Students in exceptional circumstances (health, bereavement, etc.) should contact the director of the MAS Finance program. Make sure that a few days before the deadline you have a backup printout you could hand in. Also make regular electronic backups. Computer problems at the last minute don't count as exceptional circumstances. |
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