1. komponenta

Lecture type	Total
Lectures	30
Exercises	15

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: To introduce basic numerical techniques used in finance, and specially in analysis of financial instruments and currency market products.


COURSE DESCRIPTION AND SYLLABUS:
1. Least squares problem. Regular and total least squares. Regression. Sensitivity. Regularization. Filters. Algorithms. Study examples.
2. Discretization of differential equations. Parabolic differential equations: discretization in space and time. Finite differences method: convergence, accuracy, von Neumann stability analysis, Crank-Nicolson method. Study examples, finite differences methods for Black-Scholes equation (simplified).
3. Discrete Fourier transformation, FFT. Study example.
4. Nonnegative matrices, M-matrices. Iterative methods. Study examples, Leontiev model.
5. Elements of optimization.
All study examples are carried out within tutorials in computer laboratory. The examples are implemented in MATLAB which offers maximal possibility of numerical simulations with minimal programming effort, so that the intention is focused on methods in applications. Study examples are chosen in agreement with lecturers of those courses that use techniques of numerical mathematics (Econometrics, Finance lab).

1. K. E. Atkinson: An introduction to numerical analysis, 2nd edition
2. R. Plato: Concise Numerical Mathematics
3. G. Golub, C. F. Van Loan: Matrix Computations
4. J. W. Demmel: Applied Numerical Linear Algebra
5. D. J. Higham: An introduction to financial option valuation, Mathematics, Stochastic and Computation
6. A. Iserles: A first course in the numerical analysis of differential equations

Mandatory course - Regular study - Financial and Business Mathematics