Fundamental knowledge in the field of modern financial mathematics and quantitative finance modelling. Understanding the theoretical background necessary for the quantitative analysis of financial markets under conditions of uncertainty.
- recognize the basis of financial modelling with an emphasis on applied finance
- explain stochastic calculus as a basic tool for research in modern financial mathematics
- apply basics of probability and statistics for the analysis of financial instruments in practice
- analyze testing of financial hypotheses using statistical tests
- develop theoretical basics necessary for the quantitative analysis of financial markets
- evaluate financial assets under conditions of uncertainty
Forms of Teaching
Lectures are organized through two cycles. The first cycle consists of 7 weeks of classes and mid-term exam, a second cycle of 6 weeks of classes and final exam. Classes are conducted through a total of 15 weeks with a weekly load of 3 hours.Exams
Mid-term exam. Final exam.Consultations
Consultations are organited every week.Seminars
|Type||Threshold||Percent of Grade||Threshold||Percent of Grade|
|Attendance||0 %||5 %||0 %||5 %|
|Mid Term Exam: Written||0 %||45 %||0 %|
|Final Exam: Written||0 %||50 %|
|Exam: Written||0 %||95 %|
Week by Week Schedule
- Simple and Compound Interest. Continuosly Compounded Interest. Present Value. Annuities. Amortization of a Debt.
- Comparison of Investment projects. Internal rate of return. Capital Budgeting.
- Term Structure of Interest Rates. Fixed Income Instruments.
- Zero-Coupon Bonds. Coupon Bonds. Nominal value. Maturity.
- Variable Interest Rates. Duration. Modified Duration. Portfolio of Bonds. Dynamic Hedging.
- General Term Structure. Forward rates.
- Random Walks. Brownian Motion. An Intuitive Idea of a Stochastic Process.
- Mid-term exam
- Stock Market Example. Lognormal Distribution and Lognormal Random Variables.
- Investment Strategies. The Concept of Arbitrage. Fundamental Theorem of Asset Pricing.
- Discrete Time Market Models. One period Financial Market Model. The Binomial Model.
- Risk-neutral probabilities. Lack of Arbitrage. Martingale property.
- Continuous Time Market Models. Investment Strategies. European Options. Risk-neutral Valuation.
- Black-Scholes Formula. Black-Scholes Partial Differential Equation. Market Price of Risk. Itô's Lemma.
- Final exam.