Search result: Catalogue data in Autumn Semester 2020
|Computational Science and Engineering Master|
|Fields of Specialization|
|401-3913-01L||Mathematical Foundations for Finance||W||4 credits||3V + 2U||M. Schweizer|
|Abstract||First introduction to main modelling ideas and mathematical tools from mathematical finance|
|Objective||This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It aims mainly 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.|
|Content||Topics 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 notes||Lecture notes will be made available at the beginning of the course.|
|Literature||Lecture notes will be made available at the beginning of the course. Additional (background) references are given there.|
|Prerequisites / Notice||Prerequisites: 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.
|401-4657-00L||Numerical Analysis of Stochastic Ordinary Differential Equations |
Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods"
|W||6 credits||3V + 1U||D. Salimova|
|Abstract||Course 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.|
|Objective||The 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.|
|Content||Generation 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 notes||There will be English, typed lecture notes for registered participants in the course.|
|Literature||P. 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 / Notice||Prerequisites:|
Mandatory: Probability and measure theory,
basic numerical analysis and
basics of MATLAB programming.
a) mandatory courses:
Probability Theory I.
b) recommended courses:
Start of lectures: Wednesday, September 16, 2020.
|401-8905-00L||Financial Engineering (University of Zurich)|
No enrolment to this course at ETH Zurich. Book the corresponding module directly at UZH.
UZH Module Code: MFOEC200
Mind the enrolment deadlines at UZH:
|W||6 credits||4G||University lecturers|
|Abstract||This lecture is intended for students who would like to learn more on equity derivatives modelling and pricing.|
|Objective||Quantitative models for European option pricing (including stochastic|
volatility and jump models), volatility and variance derivatives,
American and exotic options.
|Content||After introducing fundamental|
concepts of mathematical finance including no-arbitrage, portfolio
replication and risk-neutral measure, we will present the main models
that can be used for pricing and hedging European options e.g. Black-
Scholes model, stochastic and jump-diffusion models, and highlight their
assumptions and limitations. We will cover several types of derivatives
such as European and American options, Barrier options and Variance-
Swaps. Basic knowledge in probability theory and stochastic calculus is
required. Besides attending class, we strongly encourage students to
stay informed on financial matters, especially by reading daily
financial newspapers such as the Financial Times or the Wall Street
|Prerequisites / Notice||Basic knowledge of probability theory and stochastic calculus.|
|363-0561-00L||Financial Market Risks||W||3 credits||2G||D. Sornette|
|Abstract||I aim to introduce students to the concepts and tools of modern finance and to make them understand the limits of these tools, and the many problems met by the theory in practice. I will put this course in the context of the on-going financial crises in the US, Europe, Japan and China, which provide fantastic opportunities to make the students question the status quo and develop novel solutions.|
|Objective||The course explains the key concepts and mechanisms of financial economics, their depth and then stresses how and why the theories and models fail and how this is impacting investment strategies and even a global view of citizenship, given the present developing crises in the US since 2007 and in Europe since 2010.|
-Development of the concepts and tools to understand these risks and master them.
-Working knowledge of the main concepts and tools in finance (Portfolio theory, asset pricing, options, real options, bonds, interest rates, inflation, exchange rates)
-Strong emphasis on challenging assumptions and developing a systemic understanding of financial markets and their many dimensional risks
|Content||1- The Financial Crises: what is really happening? Historical perspective and what can be expected in the next decade(s). Bubbles and crashes. The illusion of he perpetual money machine.|
2- Risks in financial markets
-What is risk?
-Measuring risks of financial assets
-Introduction to three different concepts of probability
-History of financial markets, diversification, market risks
3- Introduction to financial risks and its management.
-Relationship between risk and return
-portfolio theory: the concept of diversification and optimal allocation
-How to price assets: the Capital Asset Pricing Model
-How to price assets: the Arbitrage Pricing Theory, the factor models and beyond
4- Financial markets: role and efficiency
-What is an efficient market?
-Financial markets as valuation engines: exogeneity versus endogeneity (reflexivity)
-Deviations from efficiency, puzzles and anomalies in the financial markets
-Financial bubbles, crashes, systemic instabilities
5- An introduction to Options and derivatives
-Calls, Puts and Shares and other derivatives
-Financial alchemy with options (options are building blocs of any possible cash flow)
-Determination of option value; concept of risk hedging
6-Valuation and using options
-a first simple option valuation modle
-the Binomial method for valuing options
-the Black-scholes model and formula
-practical examples and implementation
-Realized prices deviate from these theories: volatility smile and real option trading
-How to imperfectly hedge with real markets?
7- Real options
-The value of follow-on investment opportunities
-The timing option
-The abandonment option
-conceptual aspects and extensions
8- Government bonds and their valuation
-Relationship between bonds and interest rates
-Real and nominal rates of interest
-Term structure and Yields to maturity
-Explaining the term structure
-Different models of the term structure
9- Managing international risks
-The foreign exchange market
-Relations between exchanges rates and interest rates, inflation,
and other economic variables
-Hedging currency risks
-Exchange risk and international investment decisions
|Lecture notes||Lecture slides will be available on the site of the lecture|
Brealey / Myers / Allen
McGraw-Hill International Edition (2006)
+ additional paper reading provided during the lectures
|Prerequisites / Notice||none|
|401-5820-00L||Seminar in Computational Finance for CSE||W||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.
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