## Statistics of Financial Markets I (VL+UE)

## Course Description

Learn from Nobel prize winners, such as Engle (ARCH Models, 2003), Scholes, Merton, (Derivative Valuation, 1997) or Modigliani (Financial Markets Analysis, 1985) to understand statistics of financial markets!

The class is addressed to students with excellent knowledge of multivariate statistics and students with good skills in statistical software. This course is a starting point for students interested in quantitative finance and students with ambitions to work in the derivative, investment and risk-control departments. Former students of this course work for example at Deutsche Bank, Sal. Oppenheim, Citigroup, European Central Bank, BAFin, KPMG, Nadler Company and many international universities.

## Prerequisities

The course Multivariate Statistical Analysis I is required.

## Course Learning Objectives

Wiener processes, option based portfolio insurance, implied volatility dynamics, interest rate modelling, exotic options, binomial trees, option pricing, Black-Scholes model. Visit of the Frankfurt Stock Exchange.

## Course Structure

The course Statistics of Financial Markets I starts with an introduction into the basic concepts of option pricing and its stochastic foundations. After a short revision of basic statistical concepts we present the Wiener process as the core element of a probabilistic financial market model. Itô's calculus allows us to reach the first milestone of the course - the Black-Scholes (BS) European Option Pricing formula. The BS model is simple but seminal - as argued by Black in 1992: "Yet that weakness (simplicity) is also its greatest strength. People like the model because they can easily understand its assumptions . . . and if you can see the holes in the assumptions you can use the model in more sophisticated ways." This is also the main message of this part of the course - students should understand the BS model, see its strength and understand the possibility of its generalizations. The portfolio insurance (hedging) issues, concept of implied volatility, and tree-based (binomial and trinomial trees) are discussed. In addition to the European style derivatives the valuation of the American and modern Exotic derivatives are discussed. This course is not limited to the description of the models and methods but focuses on the statistical analysis, presents the applications to real financial data. In addition, important issues e.g. calibration to market data and connected numerical and statistical pitfalls are presented. The course will be structured in blocks until the end of December, some of which will be held at the university, the remainder at the Deutsche Bank, its Risk Center and PWC. At the end of the course (mid January) we will have an excursion to Frankfurt where we will have visits to Commerzbank, a FinTech and/or the ECB.

## Literature and Sources

Franke, J., Härdle, W., and Hafner, C. (2015) Statistics of Financial Markets: an Introduction. 4th ed., Springer Verlag, Heidelberg. ISBN: 978-3-642-54538-2 (555 p)

Härdle, W., Hautsch, N. and Overbeck, L. (2009) Applied Quantitative Finance. 2nd extended ed., Springer Verlag, Heidelberg. ISBN 978-3-540-69177-8 (448 p)

Hull (2005) Options, Futures, and Other Derivatives. 6th ed., Prentice Hall. ISBN 0-13-149908- 4 (816 p)

Härdle, W., Simar, L. (2015) Applied Multivariate Statistical Analysis. 4th ed., Springer Verlag, Heidelberg. ISBN 978-3-662-45170-0 (580 p)

Cizek, P., Härdle, W., Weron, R. (2011) Statistical Tools for Finance and Insurance. 2nd ed., Springer Verlag, Heidelberg. ISBN: 978-3-642-18061-3 (420 p)

** www.quantlet.de** (source codes)