Introduction to financial mathematics - BMEGT35M100

Students will learn the basics of financial time series analysis. The broad areas of knowledge covered in this course: The focus is on the practical applications of them. The primary goal is to familiarize students with the most im-portant tools and to enable them to apply them individually both in their studies and during their later work. The agenda covers the first and fourth topics (Quantitative Analysis) of the international FRM (Financial Risk Man-ager) exam to give immensely useful and practical knowledge to the audience in real life.

1. • time series analysis,
2. • basic methods of risk management,
3. • risk mitigation techniques.

1. • plan and organize independent learning,
2. • comprehend and use the professional literature of the topic,
3. • using methods learn they could perform calculations to support decision-making.

1. • is open to getting to know and adapting innovations in the financial field,
2. • collaborates with their instructors and others during the learning process,
3. • gains knowledge and information,
4. • uses the possibilities offered by IT tools

1. -

Lectures, written and oral communication, use of IT tools and techniques, optional tasks alone and in groups.

• 1. Az előadások prezentációinak anyaga, ami a félév során folyamatosan fog feltöltésre kerülni. / Slideshows of the lectures which will be uploaded continuously during the semester.
• 2. Chris Brooks (2014): Introductory Econometrics for Finance. 3rd Edtion, Cambridge University Press
• 3. Ruey S. Tsay (2010): Analysis of Financial Time Series 3rd Edition

Assessment of the learning outcomes described under 2.2. is based on two written end-term tests.

Based on written end-term tests and homework.

The written tests can be retaken in the exam period.

The written tests can be retaken in the exam period.

Bayesian Analysis: Bayes’ theorem and apply this theorem in the calculation of conditional probabilities. Apply Bayes’ theorem to scenarios with more than two possible outcomes. Time series Analysis: Introducing AR, MA, ARMA, ARIMA, ARCH and GARCH models. Highlighting the connection between AR and MA models. Emphasizing the concept of mean and variance equations. Modelling volatility I: non-linearity, volatility, variance rate, and implied volatility, the power law, the exponentially weighted moving average (EWMA) model to estimate volatility. Modelling volatility II: describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility, using the GARCH(1,1) model, mean reversion captured in the GARCH(1,1) model, the volatility term structure and the impact of volatility changes. Modelling correlation II: Gaussian copula, Student’s t-copula, multivariate copula, and one-factor copula. Simulation methods: Random number generation, Monte Carlo simulation methodes, focusing on variance reduction techniques and highlighting the problem of quasi random Real-world and risk neutral simulations, Girsanov’s theorem.