# Search result: Catalogue data in Spring Semester 2021

Quantitative Finance Master see www.msfinance.ch/index.html?/portrait/Curriculum.html 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 offering in this semester yet | ||||||

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. Marcati, A. Stein | |

Abstract | Introduction to principal methods of option pricing. Emphasis on PDE-based methods. Prerequisite MATLAB and Python 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 and Python. 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 lecture notes as well as MATLAB or Python software for registered participants in the course. | |||||

Literature | Main reference (course text): N. Hilber, O. Reichmann, Ch. Schwab and Ch. Winter: Computational Methods for Quantitative Finance, Springer Finance, Springer, 2013. Supplementary texts: 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. | |||||

Prerequisites / Notice | Knowledge of Numerical Analysis/ Scientific Computing Techniques corresponding roughly to BSc MATH or BSc RW/CSE at ETH is expected. Basic programming skills in MATLAB or Python are required for the exercises, and are _not_ taught in this course. | |||||

401-3629-00L | Quantitative Risk Management | W | 4 credits | 2V + 1U | 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, dependence structures and 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 https://people.math.ethz.ch/~patrickc/qrm | |||||

Literature | Quantitative Risk Management: Concepts, Techniques and Tools AJ McNeil, R Frey and P Embrechts Princeton University Press, Princeton, 2015 (Revised Edition) http://press.princeton.edu/titles/10496.html | |||||

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 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 www.actuaries.ch. 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 and gradient boosting machines. | |||||

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) - neural networks - credibility theory - classification and regression trees (CARTs) - bagging, random forests and boosting | |||||

Lecture notes | The lecture notes are available from: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2870308 | |||||

Prerequisites / Notice | This course will be held in English and counts towards the diploma of "Aktuar SAV". For the latter, see details under www.actuaries.ch Good knowledge in probability theory, stochastic processes and statistics is assumed. | |||||

401-4920-00L | Market-Consistent Actuarial ValuationDoes 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 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, 3rd edition. Wüthrich, M.V. EAA Series, Springer 2016. ISBN: 978-3-319-46635-4 Wüthrich, M.V., Merz, M. Claims run-off uncertainty: the full picture. SSRN Manuscript ID 2524352 (2015). England, P.D, Verrall, R.J., Wüthrich, M.V. On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins. Insurance: Mathematics and Economics 85 (2019), 74-88. 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 Cheridito, P., Ery, J., Wüthrich, M.V. Assessing asset-liability risk with neural networks. Risks 8/1 (2020), article 16. | |||||

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 www.actuaries.ch. 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). | |||||

401-4611-21L | Rough Path Theory | W | 4 credits | 2V | A. Allan, J. Teichmann | |

Abstract | The aim of this course is to provide an introduction to the theory of rough paths, with a particular focus on their integration theory and associated rough differential equations, and how the theory relates to and enhances the field of stochastic calculus. | |||||

Objective | Our first motivation will be to understand the limitations of classical notions of integration to handle paths of very low regularity, and to see how the rough integral succeeds where other notions fail. We will construct rough integrals and establish solutions of differential equations driven by rough paths, as well as the continuity of these objects with respect to the paths involved, and their consistency with stochastic integration and SDEs. Various applications and extensions of the theory will then be discussed. | |||||

Lecture notes | Lecture notes will be provided by the lecturer. | |||||

Literature | P. K. Friz and M. Hairer, A course on rough paths with an introduction to regularity structures, Springer (2014). P. K. Friz and N. B. Victoir. Multidimensional stochastic processes as rough paths, Cambridge University Press (2010). | |||||

Prerequisites / Notice | The aim will be to make the course as self-contained as possible, but some knowledge of stochastic analysis is highly recommended. The course “Brownian Motion and Stochastic Calculus” would be ideal, but not strictly required. | |||||

227-0224-00L | Stochastic SystemsDoes not take place this semester. | W | 4 credits | 2V + 1U | to be announced | |

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 www.actuaries.ch. Basic knowledge in probability theory is assumed, in particular conditional expectations. | |||||

252-0220-00L | Introduction to Machine Learning Limited number of participants. Preference is given to students in programmes in which the course is being offered. All other students will be waitlisted. Please do not contact Prof. Krause for any questions in this regard. If necessary, please contact studiensekretariat@inf.ethz.ch | W | 8 credits | 4V + 2U + 1A | A. Krause, F. Yang | |

Abstract | The course introduces the foundations of learning and making predictions based on data. | |||||

Objective | The course will introduce the foundations of learning and making predictions from data. We will study basic concepts such as trading goodness of fit and model complexitiy. We will discuss important machine learning algorithms used in practice, and provide hands-on experience in a course project. | |||||

Content | - Linear regression (overfitting, cross-validation/bootstrap, model selection, regularization, [stochastic] gradient descent) - Linear classification: Logistic regression (feature selection, sparsity, multi-class) - Kernels and the kernel trick (Properties of kernels; applications to linear and logistic regression); k-nearest neighbor - Neural networks (backpropagation, regularization, convolutional neural networks) - Unsupervised learning (k-means, PCA, neural network autoencoders) - The statistical perspective (regularization as prior; loss as likelihood; learning as MAP inference) - Statistical decision theory (decision making based on statistical models and utility functions) - Discriminative vs. generative modeling (benefits and challenges in modeling joint vy. conditional distributions) - Bayes' classifiers (Naive Bayes, Gaussian Bayes; MLE) - Bayesian approaches to unsupervised learning (Gaussian mixtures, EM) | |||||

Literature | Textbook: Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press | |||||

Prerequisites / Notice | Designed to provide a basis for following courses: - Advanced Machine Learning - Deep Learning - Probabilistic Artificial Intelligence - Seminar "Advanced Topics in Machine Learning" | |||||

401-3932-19L | Machine Learning in Finance | W | 6 credits | 3V + 1U | J. Teichmann | |

Abstract | The course will deal with the following topics with rigorous proofs and many coding excursions: Universal approximation theorems, Stochastic gradient Descent, Deep networks and wavelet analysis, Deep Hedging, Deep calibration, Different network architectures, Reservoir Computing, Time series analysis by machine learning, Reinforcement learning, generative adversersial networks, Economic games. | |||||

Objective | ||||||

Prerequisites / Notice | Bachelor in mathematics, physics, economics or computer science. | |||||

363-1114-00L | Introduction to Risk Modelling and Management | W | 3 credits | 2V | H. Schernberg, B. J. Bergmann, D. N. Bresch | |

Abstract | This course is a practical, hands-on introduction to various aspects of modelling, dealing with and managing risks across different industries, contexts and applications. | |||||

Objective | Our main goal is helping students understand what is required of the 21st century’s risk manager. To do so, the course provides a qualitative and quantitative introduction to the various risks that societies and businesses face and to their management. The course encourages students to think critically about models and mathematical representations of risks. Finally, it aims at conveying the current challenges of managing today’s risks given available technologies. After taking this course, students should be able to identify and formulate a risk analysis problem with quantitative methods in a particular field. | |||||

Content | The course describes the building blocks of risk modelling: uncertainty, vulnerability, resilience, decision-making under uncertainty. It examines at different approaches to modelling and dealing with as well as mitigating different kind of risks in different industries. The lectures emphasize the decision-making processes in various business and how risk-management relates to the value chain of a company. Cases range from enterprise risk management, natural catastrophes, climate risk, energy market risk, risk engineering, financial risks, operational risk, cyber risk and more. Moreover, the course highlights the data-driven approach to smart algorithms applied to risk modelling and management. The panel of lecturers comprises risk professionals from various industries and government as well as academics from different disciplines. The course covers the following areas: 1. Fundamentals of Risk Modelling: Probability, Uncertainty, Vulnerability, Decision-Making under Uncertainty 2. Fundamentals of Risk Management and Enterprise Risk Management 3. Risk Modelling and Management across Different Areas, with invited speakers The list of past speakers can be found here: Link | |||||

Lecture notes | The course materials are provided via the Moodle application. | |||||

Literature | Additional readings will be discussed during the lectures. | |||||

Prerequisites / Notice | The course is opened to students from all backgrounds. Some experience with quantitative disciplines such as probability and statistics, however, is useful. | |||||

363-1153-00L | New Technologies in Banking and Finance | W | 3 credits | 2V | B. J. Bergmann, P. Cheridito, H. Gersbach, P. Mangold, J. Teichmann, R. Wattenhofer | |

Abstract | Technological advances, digitization and the ability to store and process vast amounts of data has changed the landscape of banking and finance in recent years. This course will unpack the technologies underlying these transformations and reflect on the impacts on the financial world, covering also change management perspectives. | |||||

Objective | After taking this course, students will be able to - Understand recent technological developments and how they drive transformation in banking and finance - Understand the challenges of this digital transformation when managing financial and non-financial risks - Reflect on the impacts this transformation has on workflows, agile working, project and change management | |||||

Content | The financial manager of the future is commanding a wide set of skills ranging from a profound understanding of technological advances and a sensible understanding of the impact on workflows and business models. Students with an interest in finance and banking are invited to take the course without explicit theoretical knowledge in financial economics. As the course will cover topics like machine learning, cyber security, distributed computing, and more, an understanding of these technologies is welcomed, however not mandatory. The course will also go beyond technological advances and will also cover management-related contents. The course is divided in sections, each covering different areas and technologies. Students are asked to solve small cases in groups for each section. Invited guest speakers will contribute to the sessions. In addition, separate networking sessions will provide entry opportunities into finance and banking. More information on the speakers and specific session can be found here: https://riskcenter.ethz.ch/education/lectures.html and on the moodle page. | |||||

Prerequisites / Notice | The course is opened to students from all backgrounds. Some experience with quantitative disciplines such as probability and statistics, however, is useful. | |||||

Master's Thesis |

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