The spring semester 2021 will certainly take place online until Easter. Exceptions: Courses that can only be carried out with on-site presence. Please note the information provided by the lecturers.

Search result: Catalogue data in Autumn Semester 2018

Quantitative Finance Master Information
see www.msfinance.ch/index.html?/portrait/Curriculum.html

Students in the Joint Degree Master's Programme "Quantitative Finance" must book University of Zurich modules directly at the University of Zurich. Those modules are not listed here.
Core Courses
Economic Theory for Finance
For possible additional course offerings see www.msfinance.ch
Mathematical Methods for Finance
For possible additional course offerings see www.msfinance.ch
NumberTitleTypeECTSHoursLecturers
401-3913-01LMathematical Foundations for Finance Information W4 credits3V + 2UE. W. Farkas, M. Schweizer
AbstractFirst introduction to main modelling ideas and mathematical tools from mathematical finance
ObjectiveThis course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest.. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.
ContentTopics to be covered include

- financial market models in finite discrete time
- absence of arbitrage and martingale measures
- valuation and hedging in complete markets
- basics about Brownian motion
- stochastic integration
- stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem
- Black-Scholes formula
Lecture notesLecture notes will be sold at the beginning of the course.
LiteratureLecture notes will be sold at the beginning of the course. Additional (background) references are given there.
Prerequisites / NoticePrerequisites: Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely. Especially participants without a direct mathematics background are strongly advised to familiarise themselves with those tools before (or very quickly during) the course. (A possible alternative to the above English textbook are the (German) lecture notes for the standard course "Wahrscheinlichkeitstheorie".)

For those who are not sure about their background, we suggest to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared.
Elective Courses
Economic Theory for Finance
For possible additional course offerings see www.msfinance.ch
NumberTitleTypeECTSHoursLecturers
401-4633-00LData Analytics in Organisations and BusinessW5 credits2V + 1UI. Flückiger
AbstractOn the end-to-end process of data analytics in organisations & business and how to transform data into insights for fact based decisions. Presentation of the process from the beginning with framing the business problem to presenting the results and making decisions by the use of data analytics. For each topic case studies from the financial service, healthcare and retail sectors will be presented.
ObjectiveThe goal of this course is to give the students the understanding of the data analytics process in the business world, with special focus on the skills and techniques used besides the technical skills. The student will become familiar with the "business language", current problems and thinking in organisations and business and tools used.
ContentFraming the Business Problem
Framing the Analytics Problem
Data
Methodology
Model Building
Deployment
Model Lifecycle
Soft Skills for the Statistical/Mathematical Professional
Lecture notesLecture Notes will be available.
Prerequisites / NoticePrerequisites: Basic statistics and probability theory and regression
363-1081-00LAsset Liability Management and Treasury Risks Restricted registration - show details
Number of participants limited to 40.
W3 credits2VP. Mangold, M. Eichhorn
AbstractAsset Liability Management (ALM) is key to the financial success of any corporation. The goal is to develop a comprehensive understanding of the nature of corporate balance sheet and off-balance sheet positions and related profits and losses, including identification and mitigation of undue risks taken. This course is geared towards preparing students to apply these concepts in practical settings.
ObjectiveThe main learning objectives of this course are:
- develop a comprehensive understanding of the nature of corporate balance sheet and off-balance sheet positions and their respective contribution to profits and losses
- measure and assess exposures to risk factors such as interest and FX rates, equity and commodity prices, as well as liquidity events
- trading and hedging to mitigate undue risks incurred
ContentThe course is organized around a series of case studies. We will first discuss and develop an understanding of the fundamentals on different aspects of the management and risk management of the balance sheet. Using real life case studies each concept will then be directly applied and tested. In-class discussions, presentations and one written assignment are used to facilitate active and interactive learning in a stimulating environment. During the case studies students will frequently work in small groups. Therefore, the number of participants is limited to 40.

The course focuses on the application of finance concepts to the financial management of corporations and is geared towards preparing students to apply these concepts in practical settings. Executives of all sectors are expected to have a sound understanding of the content covered. As such, the course is not exclusively targeted at students who are considering a career in the financial services sector. It also recommended for students who want to work in the finance, treasury or risk area of corporates. It is also suitable for students who want to work for a consultancy firm.
LiteratureNo single textbook covers the course, below we list some useful references. Further materials will be made available to students prior to the lectures

Choudhry, M. 2012. The Principles of Banking. Wiley Finance.
Marrison, C. 2002. The Fundamentals of Risk Measurement. McGraw-Hill.
Bohn, A. & Elkenbracht-Huizing, M. 2017. The Handbook of ALM in Banking (2nd edition).
Prerequisites / NoticeParticipants should have a basic understanding of financial management, gained, for example, from prior undergraduate economics, business, or accounting studies.
Mathematical Methods for Finance
For possible additional course offerings see www.msfinance.ch
NumberTitleTypeECTSHoursLecturers
401-3925-00LNon-Life Insurance: Mathematics and Statistics Information W8 credits4V + 1UM. V. Wüthrich
AbstractThe lecture aims at providing a basis in non-life insurance mathematics which forms a core subject of actuarial sciences. It discusses collective risk modeling, individual claim size modeling, approximations for compound distributions, ruin theory, premium calculation principles, tariffication with generalized linear models, credibility theory, claims reserving and solvency.
ObjectiveThe student is familiar with the basics in non-life insurance mathematics and statistics. This includes the basic mathematical models for insurance liability modeling, pricing concepts, stochastic claims reserving models and ruin and solvency considerations.
ContentThe following topics are treated:
Collective Risk Modeling
Individual Claim Size Modeling
Approximations for Compound Distributions
Ruin Theory in Discrete Time
Premium Calculation Principles
Tariffication and Generalized Linear Models
Bayesian Models and Credibility Theory
Claims Reserving
Solvency Considerations
Lecture notesM. V. Wüthrich, Non-Life Insurance: Mathematics & Statistics
http://ssrn.com/abstract=2319328
Prerequisites / NoticeThe 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 www.actuaries.ch.

Prerequisites: knowledge of probability theory, statistics and applied stochastic processes.
401-4889-00LMathematical Finance Information W11 credits4V + 2UM. Schweizer
AbstractAdvanced course on mathematical finance:
- semimartingales and general stochastic integration
- absence of arbitrage and martingale measures
- fundamental theorem of asset pricing
- option pricing and hedging
- hedging duality
- optimal investment problems
- additional topics
ObjectiveAdvanced course on mathematical finance, presupposing good knowledge in probability theory and stochastic calculus (for continuous processes)
ContentThis is an advanced course on mathematical finance for students with a good background in probability. We want to give an overview of main concepts, questions and approaches, and we do this mostly in continuous-time models.

Topics include
- semimartingales and general stochastic integration
- absence of arbitrage and martingale measures
- fundamental theorem of asset pricing
- option pricing and hedging
- hedging duality
- optimal investment problems
- and probably others
Lecture notesThe course is based on different parts from different books as well as on original research literature.

Lecture notes will not be available.
Literature(will be updated later)
Prerequisites / NoticePrerequisites are the standard courses
- Probability Theory (for which lecture notes are available)
- Brownian Motion and Stochastic Calculus (for which lecture notes are available)
Those students who already attended "Introduction to Mathematical Finance" will have an advantage in terms of ideas and concepts.

This course is the second of a sequence of two courses on mathematical finance. The first course "Introduction to Mathematical Finance" (MF I), 401-3888-00, focuses on models in finite discrete time. It is advisable that the course MF I is taken prior to the present course, MF II.

For an overview of courses offered in the area of mathematical finance, see Link.
401-4657-00LNumerical Analysis of Stochastic Ordinary Differential Equations Information
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
W6 credits3V + 1UA. Jentzen, L. Yaroslavtseva
AbstractCourse on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables.
ObjectiveThe aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.
ContentGeneration of random numbers
Monte Carlo methods for the numerical integration of random variables
Stochastic processes and Brownian motion
Stochastic ordinary differential equations (SODEs)
Numerical approximations of SODEs
Applications to computational finance: Option valuation
Lecture notesLecture notes are available as a PDF file: see Learning materials.
LiteratureP. Glassermann:
Monte Carlo Methods in Financial Engineering.
Springer-Verlag, New York, 2004.

P. E. Kloeden and E. Platen:
Numerical Solution of Stochastic Differential Equations.
Springer-Verlag, Berlin, 1992.
Prerequisites / NoticePrerequisites:

Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.

a) mandatory courses:
Elementary Probability,
Probability Theory I.

b) recommended courses:
Stochastic Processes.

Start of lectures: Wednesday, September 19, 2018.

Date of the End-of-Semester examination: Wednesday, December 19, 2018, 13:00-15:00; students must arrive before 12:30 at ETH HG E 19.
Room for the End-of-Semester examination: ETH HG E 19.

Exam inspection: Tuesday, February 26, 2019,
12:00-13:00 at HG D 7.2.
Please bring your legi.
401-3929-00LFinancial Risk Management in Social and Pension Insurance Information W4 credits2VP. Blum
AbstractInvestment returns are an important source of funding for social and pension insurance, and financial risk is an important threat to stability. We study short-term and long-term financial risk and its interplay with other risk factors, and we develop methods for the measurement and management of financial risk and return in an asset/liability context with the goal of assuring sustainable funding.
ObjectiveUnderstand the basic asset-liability framework: essential principles and properties of social and pension insurance; cash flow matching, duration matching, valuation portfolio and loose coupling; the notion of financial risk; long-term vs. short-term risk; coherent measures of risk.

Understand the conditions for sustainable funding: derivation of required returns; interplay between return levels, contribution levels and other parameters; influence of guaranteed benefits.

Understand the notion of risk-taking capability: capital process as a random walk; measures of long-term risk and relation to capital; short-term solvency vs. long-term stability; effect of embedded options and guarantees; interplay between required return and risk-taking capability.

Be able to study empirical properties of financial assets: the Normal hypothesis and the deviations from it; statistical tools for investigating relevant risk and return properties of financial assets; time aggregation properties; be able to conduct analysis of real data for the most important asset classes.

Understand and be able to carry out portfolio construction: the concept of diversification; limitations to diversification; correlation breakdown; incorporation of constraints; sensitivities and shortcomings of optimized portfolios.

Understand and interpret the asset-liability interplay: the optimized portfolio in the asset-liability framework; short-term risk vs. long-term risk; the influence of constraints; feasible and non-feasible solutions; practical considerations.

Understand and be able to address essential problems in asset / liability management, e.g. optimal risk / return positioning, optimal discount rate, target value for funding ratio or turnaround issues.

Have an overall view: see the big picture of what asset returns can and cannot contribute to social security; be aware of the most relevant outcomes; know the role of the actuary in the financial risk management process.
ContentFor pension insurance and other forms of social insurance, investment returns are an important source of funding. In order to earn these returns, substantial financial risks must be taken, and these risks represent an important threat to financial stability, in the long term and in the short term.

Risk and return of financial assets cannot be separated from one another and, hence, asset management and risk management cannot be separated either. Managing financial risk in social and pension insurance is, therefore, the task of reconciling the contradictory dimensions of

1. Required return for a sustainable funding of the institution,
2. Risk-taking capability of the institution,
3. Returns available from financial assets in the market,
4. Risks incurred by investing in these assets.

This task must be accomplished under a number of constraints. Financial risk management in social insurance also means reconciling the long time horizon of the promised insurance benefits with the short time horizon of financial markets and financial risk.

It is not the goal of this lecture to provide the students with any cookbook recipes that can readily be applied without further reflection. The goal is rather to enable the students to develop their own understanding of the problems and possible solutions associated with the management of financial risks in social and pension insurance.

To this end, a rigorous intellectual framework will be developed and a powerful set of mathematical tools from the fields of actuarial mathematics and quantitative risk management will be applied. When analyzing the properties of financial assets, an empirical viewpoint will be taken using statistical tools and considering real-world data.
Lecture notesExtensive handouts will be provided. Moreover, practical examples and data sets in Excel and R will be made available.
Prerequisites / NoticeSolid base knowledge of probability and statistics is indispensable. Specialized concepts from financial and insurance mathematics as well as quantitative risk management will be introduced in the lecture as needed, but some prior knowledge in some of these areas would be an advantage.

This course counts towards the diploma of "Aktuar SAV".

The exams ONLY take place during the official ETH examination period.
401-3922-00LLife Insurance MathematicsW4 credits2VM. Koller
AbstractThe classical life insurance model is presented together with the important insurance types (insurance on one and two lives, term and endowment insurance and disability). Besides that the most important terms such as mathematical reserves are introduced and calculated. The profit and loss account and the balance sheet of a life insurance company is explained and illustrated.
Objective
401-3928-00LReinsurance AnalyticsW4 credits2VP. Antal, P. Arbenz
AbstractThis course provides an actuarial introduction to reinsurance. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical models for extreme events such as natural or man-made catastrophes. The lecture covers reinsurance contracts, Experience and Exposure pricing, natural catastrophe modelling, solvency regulation, and alternative risk transfer
ObjectiveThis course provides an introduction to reinsurance from an actuarial point of view. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes.
Topics covered include:
- Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business.
- Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models
- Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks
- Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context
- Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2
- Alternative Risk Transfer: Alternatives to traditional reinsurance such as insurance linked securities and catastrophe bonds
ContentThis course provides an introduction to reinsurance from an actuarial point of view. The objective is to understand the fundamentals of risk transfer through reinsurance, and the mathematical approaches associated with low frequency high severity events such as natural or man-made catastrophes.
Topics covered include:
- Reinsurance Contracts and Markets: Different forms of reinsurance, their mathematical representation, history of reinsurance, and lines of business.
- Experience Pricing: Modelling of low frequency high severity losses based on historical data, and analytical tools to describe and understand these models
- Exposure Pricing: Loss modelling based on exposure or risk profile information, for both property and casualty risks
- Natural Catastrophe Modelling: History, relevance, structure, and analytical tools used to model natural catastrophes in an insurance context
- Solvency Regulation: Regulatory capital requirements in relation to risks, effects of reinsurance thereon, and differences between the Swiss Solvency Test and Solvency 2
- Alternative Risk Transfer: Alternatives to traditional reinsurance such as insurance linked securities and catastrophe bonds
Lecture notesSlides, lecture notes, and references to literature will be made available.
Prerequisites / NoticeBasic knowledge in statistics, probability theory, and actuarial techniques
401-4912-11LTrends in Stochastic Portfolio TheoryW4 credits2VM. Larsson
AbstractThis course presents an introduction to Stochastic Portfolio Theory, which
provides a mathematical framework for studying and exploiting empirically
observed regularities of large equity markets. A central goal of the theory is
to describe certain forms of arbitrage that arise over sufficiently long time
horizons.
Objective
ContentThis course presents an introduction to Stochastic Portfolio Theory, which
provides a mathematical framework for studying and exploiting empirically
observed regularities of large equity markets. A central goal of the theory is
to describe certain forms of arbitrage that arise over sufficiently long time
horizons. Since it was first introduced by Robert Fernholz almost 20 years ago,
the theory has experienced rapid developments. This course will cover the
foundations of Stochastic Portfolio Theory, including topics like relative
arbitrage, functional portfolio generation, and capital distribution curves, as
well as more recent developments.
Prerequisites / NoticePrerequisites: Familiarity with Ito calculus at the level of Brownian Motion
and Stochastic Calculus. Some background in mathematical finance is helpful.

A course with similar content was offered in HS 2015 under the title "New Trends in Stochastic Portfolio Theory".
Master's Thesis
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