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Track: Quantitative Methods in Finance

Track director: Prof. Dr. S. Rachev

ECTS = 8


Lectures:

• Financial Econometrics
• Stochastic Calculus and Introduction to Mathematical Finance

Track description:

The track “Quantitative Methods in Finance” covers two major fields of financial analysis: financial data analysis (Financial Econometrics), and valuation of  "fair" prices of the underlying financial instruments (Mathematical Finance).

Financial Econometrics provides a comprehensive study of financial data: modeling, estimation, model testing and forecasting. It starts with a rigorous description of  stationary and non-stationary time series models (e.g., ARMA(p, q) and ARIMA(p, d, q) models), non-linearity, trends and volatility in financial data (e.g., ARCH and GARCH models); co-integration and error-correction models, followed by estimation, model verification and forecasting. As applications of the built-in reliable econometric models, the course continues with the study of the predictability of asset returns, market microstructure (analysis of high-frequency data), cross-sectional regression models, multifactor pricing models, present-value relations and rational bubbles, market frictions, and estimation and fitting of the term structure of interest rates.

Mathematical Finance uses the modern stochastic calculus as a main tool. With that basis, the course provides one- and multi-period pricing models based on the notions of arbitrage and completeness. The course continues with the description of state price vectors, valuations of assets and portfolios, contingent claims, pricing for discrete-time markets, and hedging the risk of liabilities and pricing it. In continuous time, the securities valuation results are extended to continuous and jump diffusion models, term-structure of interest rates, and the valuation of complex financial instruments. The course covers the important issues of hedging the risk of liabilities and pricing it. The basis of Mathematical Finance is the Arbitrage Pricing Theory, which together with the Capital Asset Pricing Model and General Equilibrium Theory, provides the pillars of modern theory of finance.

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