Mathematical and Quantitative Finance

The course covers the concepts and practice of mathematical

and quantitative finance.

Among the topics considered are:

• (Generalized) Wiener Process, Poisson Process, other Levy processes; simulation and visualization of solutions to SDEs driven by such processes

• elementary stochastic calculus, Ito's Lemma, Geometric Brownian Motion, Monte Carlo approximation of expectations, probabilities, etc

• Black-Scholes equation, Feynman-Kac formula, risk-neutral valuation

• valuation of different types of options based on formulae and Monte-Carlo simulations, jump diffusion

• martingales and measures

• interest rates, models of the short rate, HJM model

• credit risk, Merton's model and copulas

• overview of (conditional) volatility modelling, bootstrap

• Value-At-Risk

• selected state-of-the-art approaches (eg, wavelets, functional data analysis, self-organizing map)

R (simulations and analyses) and RMarkdown (generation of documents with text and code) are used in rstudio https://rstudio.com/(Avautuu uuteen välilehteen) in the course.

Course participants are supposed to acquire hand-on experience with R by applying various techniques of mathematical and quantitative

finance to synthetic and real data. No prior knowledge of programming is required.