Syllabus
Registration via LPIS
Day | Date | Time | Room |
---|---|---|---|
Tuesday | 05/11/21 | 09:00 AM - 01:00 PM | Online-Einheit |
Tuesday | 05/18/21 | 09:00 AM - 01:00 PM | Online-Einheit |
Tuesday | 05/25/21 | 09:00 AM - 01:00 PM | Online-Einheit |
Tuesday | 06/01/21 | 09:00 AM - 01:00 PM | Online-Einheit |
Tuesday | 06/08/21 | 09:00 AM - 01:00 PM | Online-Einheit |
Tuesday | 06/15/21 | 09:00 AM - 01:00 PM | Online-Einheit |
Tuesday | 06/22/21 | 09:00 AM - 12:00 PM | Online-Einheit |
Friday | 06/25/21 | 10:00 AM - 12:00 PM | Online-Einheit |
This lecture discusses the basic mathematical tools for continuous-time finance and applies these to problems in derivative pricing. In particular we study option pricing in the Black Scholes model.
We will cover the following topics
- Wiener process
- Quadratic variation
- Pathwise Ito calculus, elementary Ito integral and the Ito formula
- Generators and Feynman Kac for one-dimensional diffusions
- Derivative pricing via replication in the Black Scholes model
- Black Scholes formula and application
- Extensions beyond the classical Black Scholes model
- Basic numeric approaches for option pricing
Continuous time finance is concerned with: Brownian motion, stochastic calculus, risk-neutral pricing, stochastic and partial differential equations, exotic options.
After completing this class the student will have the ability to:
• describe the basic concepts and methods of continuous time finance;
• apply and do computational work with the basic concepts and definitions of continuous time finance.
After completing this class the student will also have the ability to:
• confidently apply ideas of continuous time finance in doing analytical work for financial markets.
• solve applied problems where skills are required from continuous time finance.
no formal requirements but attendance is strongly recommended (due to distance learning)
The course consists of several parts: overview presentations of the key elements via ZOOMduring lecture hours (usually Tuesday, 10-12.15), a tutorium where exercises are discussed (usually Tuesday 9-10), solution of exercises and self-study of the course material provided (slides and lecture notes).
Midterm Test 25% (remote take home)
Exercise Series (25%) (remote take home)
Final exam is written (online supervision) and an optional oral exam (50%)
A minimum score of 45% in the final exam and an overall score of 50 % is necessary for passing. The final exam consists of two parts: a mandatory written test and an oral test. The oral test is optional and can be taken only by students who obtained at least 80% of the points in the rest of the course and who want to obtain the grade "excellent" (but note that a bad performance in the final can also lead to a deterioration of your grade) .
Exercises will be discussed during the tutorium (also additional exercises).
• Advanced Business Mathematics (class Mathematics I of the QFin program);
• Advanced Business Probability theory (class Probability of the QFin program);
.
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