Financial Markets Data Processing

Vztahy:

The course 18ZDFT can be graded only after the course 18TFT has been successfully completed.

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Software Engineering

Synopsis:

The course enables students to combine knowledge of numerical methods, Matlab programming and financial mathematics to solve practical problems in finance such as portfolio optimization, risk management and valuation of financial derivatives, especially options of different types. Upon completion of the course the student will be able to formulate and numerically solve concrete problems in the given field and subsequently implement their solutions in practice.

Requirements:

Knowledge of programming in Matlab and numerical methods, fundamentals of financial mathematics, ie completion of the subject Theory of Financial Markets.

Syllabus of lectures:

1. Introduction to Numerical Computations in Financial Mathematics

2. Numerical solution of a system of linear equations and its use for valuation of assets

3. Non-linear systems of equations and use of polynomials in financial mathematics

4. Finite differences method and its use for asset valuation

5. Linear programming and its use to optimize the portfolio

6. Dynamic programming in financial mathematics

7. Non-Convex Optimization and Portfolio Management

8. Binomial and trinomic tree including use for valuation of options

9. Numerical solution of stochastic differential equation and valuation of options

10. Monte Carlo Simulation and Valuation of Financial Assets

11. Modeling the time structure of the interest rate

12. Modeling of stochastic volatility

13. Heuristic methods and their use in finance

Syllabus of tutorials:

The structure of exercises is identical to lectures. Exercises are focused on typical problems from each topic.

1. Introduction to Numerical Computations in Financial Mathematics

2. Numerical solution of a system of linear equations and its use for valuation of assets

3. Non-linear systems of equations and use of polynomials in financial mathematics

4. Finite differences method and its use for asset valuation

5. Linear programming and its use to optimize the portfolio

6. Dynamic programming in financial mathematics

7. Non-Convex Optimization and Portfolio Management

8. Binomial and trinomic tree including use for valuation of options

9. Numerical solution of stochastic differential equation and valuation of options

10. Monte Carlo Simulation and Valuation of Financial Assets

11. Modeling the time structure of the interest rate

12. Modeling of stochastic volatility

13. Heuristic methods and their use in finance

Study Objective:

an overview of numerical methods and their use for valuation of financial assets, basics of portfolio optimization and risk management.

Study materials:

Mandatory reading

[1] M. Gilli, D. Maringer, E Schumann: Numerical Methods and Optimization in Finance, Elsevier, Oxford, 2011.

Recommended reading

[2] P. Brandimarte: Numerical Methods in Finance and Economics: A MATLAB-Based Introduction. Berlin: Springer-Verlag, 2006.

[3] G. Fusai, A. Roncoroni: Implementing Models in Quantitative Finance: Methods and Cases. Berlin: Springer, 2008.

[4] J. Miller, D. Edelman, J. Appleby: Numerical Methods for Finance. London: Chapman & Hall, 2007.

[5] J. Cornuejols, R. Tutuncu: Optimization Methods in Finance. Carnegie Mellon University, 2006.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikace softwarového inženýrství (elective course)
• Aplikované matematicko-stochastické metody (elective course)
• Aplikace informatiky v přírodních vědách (elective course)