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2022/2023 KAN-CMECV1250U Mathematical Finance 2: Continuous Time Finance
| English Title | |
| Mathematical Finance 2: Continuous Time Finance |
Course information |
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| Language | English |
| Course ECTS | 7.5 ECTS |
| Type | Elective |
| Level | Full Degree Master |
| Duration | One Quarter |
| Start time of the course | Second Quarter |
| Timetable | Course schedule will be posted at calendar.cbs.dk |
| Max. participants | 80 |
| Study board |
Study Board for HA/cand.merc. i erhvervsøkonomi og matematik,
MSc
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| Last updated on 10-02-2022 | |
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| Learning objectives | ||||||||||||||||||||||||||||||
| By the end of the course, students will be
confident with the probabilistic techniques required to understand
the most widely used models in finance, from the Black-Scholes
model to stochastic volatility models and affine term structure
models.
To achieve the grade 12, students should meet the following learning objectives with no or only minor mistakes or errors:
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| Course prerequisites | ||||||||||||||||||||||||||||||
| Prerequisites at the level of HA(mat.). It is an advantage to have followed Matematisk Finansiering 1, but it is not a prerequisite. The course includes a voluntary Introductory Python Workshop consisting of Jupyter notebooks and exercises. | ||||||||||||||||||||||||||||||
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Over the last few years, financial analysts have used more and more sophisticated mathematical concepts to describe the behaviour of markets or to derive computing methods. This course provides an intro- duction to stochastic calculus and shows how it can be applied to the pricing and hedging of financial contracts, such as equity options and interest rate derivatives. The goal is to make students confident with the probabilistic techniques required to understand the most widely used financial models. The course is mainly suitable for students who would like to become quantitative analysts, asset managers, traders, risk managers, structurers, or who are simply generally interested in financial markets and want to gain the technical skills needed to understand and model their behaviour.
The course is split into 4 sections:
1. Discrete Time Finance: the binomial model
2. Introduction to Stochastic Processes and Stochastic Calculus
3. Pricing and Hedging in Continuous Time
4. Advanced material
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| Description of the teaching methods | ||||||||||||||||||||||||||||||
| The pedagogical approach of the course is applied
in nature. That means will we will abstract from much of the (deep)
technical rigour underlying continuous time theory and instead
concentrate on applications and problem solving. In other words, we
will be ‘learning-by-doing’, which will require investing time in
problem sets and getting our hands dirty with data and coding
exercises:
- Real life trading resource: At the beginning of the course you will all receive an invitation for a real-time trading account within the student lab at Interactive Brokers: www.interactivebrokers.co.uk Your accounts will be charged with USD 1,000,000 in paper trading equity. Account equity will fluctuate as if trades were executed in the real market and you can trade stocks, options, futures, bonds and currencies, and credit default swaps. We will use this as a resource for real world pricing, calibration exercises, risk management and speculative (trading) exercises - Coding: The financial industry is increasingly adopting Python and recent recruitment trends suggest that Python will soon become the de-facto programming language for quantitative analysis in finance. The benefits of Python with respect to its competitors is are that it is (a) easy to learn, read and write; (b) is a high-level programming language; (c) fast and easily scalable; (d) has vast library support; (e) is free and open source. This course include an introductory set of lectures in Python for financial analysis. We will begin with the basics such as installation, an overview of the programming environment and tips on how to code ‘Pythonically’. You will learn the fundamentals of Python variables, loops, functions, data structures and learn powerful methods to efficiently practice data science and visualise data. |
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| Feedback during the teaching period | ||||||||||||||||||||||||||||||
| Each lecture will consist of a set of slides
Exercise sets will be regularly distributed and selected problems solved in class Solutions will be provided There will be a voluntary mid-term assignment that will test students on course material. Feedback will be given. |
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The course can be taken by any interested student
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| Expected literature | ||||||||||||||||||||||||||||||
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Main course textbooks are:
``Stochastic Calculus for Finance II: Continuous-time Models'' , (2004) Shreve ``Arbitrage Theory in Continuous Time'', Björk (2020)
(The books are available online through CBS library)
Hand outs from selected chapters of:
``Options, Futures and Other Derivatives'' (8th edition or later), John Hull ``Stochastic Calculus for Finance: Discrete-time Models'', (2004) Shreve ``A Course in Derivative Securities'', Kerry Back (2005) ``Fixed Income Securities: Valuation, Risk, and Risk Management'', Pietro Veronesi (2010)
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