FINANCIAL MATHEMATICS | Postgraduate Program in Financial Management Engineering

FINANCIAL MATHEMATICS

Διδάσκοντας/ουσα: 
Βασίλειος Κούτρας
Κωδικός Μαθήματος: 
I-5
Τύπος Μαθήματος: 
Υποχρεωτικό Μάθημα Κατεύθυνσης
Έτος Σπουδών: 
Α'
Εξάμηνο Σπουδών: 
Χειμερινό
Αριθμός Πιστωτικών Μονάδων (ECTS): 
6
Γλώσσα Διδασκαλίας: 
Greek
Περιγραφή: 

The goal of the course is twofold: firstly, to introduce students to the basic principles governing financial modeling and analysis, and secondly, to provide an in-depth understanding of advanced mathematical concepts and techniques for applying them in the solution of both theoretical and practical problems. Additionally, it aims to provide the necessary background either for the comprehension of subsequent courses in the study program or for further study.

Προαπαιτήσεις: 

None

Περιεχόμενο του μαθήματος (Syllabus): 
  1. Probability Theory: Random variables, probability distributions, mean and variance. The normal distribution. Conditional probability distribution, joint probability distribution, independence, covariance and correlation.
  2. Statistics: Sample, sampling distribution. Estimation (point and interval estimation), hypothesis testing.
  3. Introduction and basic concepts: Financial securities and financial markets, types of financial assets (stocks, bonds, derivative products), interest & interest rate, simple, discount and compound interest, time value of money, present and future value, net present value.
  4. Financial risk & uncertainty Ι: Return (arithmetic and logarithmic), the return as a random variable, return on single investment and portfolio, expected return, expected return on portfolio with N assets.  The concept of risk & financial risk, major types of financial risk, risk measures, the variance as a risk measure, portfolio risk and covariance structure, systematic and non-systematic risk, risk diversification.
  5. Financial risk & uncertainty ΙI: Introduction to  Value-at-Risk (VaR) and Expected Shortfall, calculation of VaR, Normal VaR, Historical VaR.
  6. Introduction to Derivative Pricing - One-Period Binomial Model: Pricing Forwards and Futures, pricing of options - one-period binomial model, changing the probability measure, the 'risk-neutral world,' relationships between the prices of different option contracts.
  7. Advanced Probability Concepts – Martingales: σ-algebra and measure, stochastic independence, conditional mean, properties of conditional mean, stochastic process, martingales.
  8. Valuation of Options in Discrete Time - Multi-Period Binomial Model: Self-financing investment strategy in discrete time, n-period binomial model, no-arbitrage pricing of derivative financial products using an n-period model.
  9. Brownian Motion: Brownian Motion, Geometric Brownian Motion.
  10. Valuation of Options in Continuous Time – The Black-Scholes-Merton (BSM) Model: The Black-Scholes-Merton model, practical issues with the Black-Scholes-Merton formula, Delta Hedging strategy, option pricing by solving the BSM equation in Excel.
Συνιστώμενη Βιβλιογραφία προς μελέτη: 

 

  • An Elementary Introduction to Mathematical Finance: Options and other Topics, Ross, S., Cambridge University Press; 2nd edition, 2002.
  • Options, Futures and Other Derivatives, Ηull, J., 5th  edition, Prentice Hall, 2003.
  • The Mathematics of Financial Derivatives, Willmott, P., Howison, S., Dewynne, J., Cambridge University Press,1997.
  • An Introduction to the Mathematics of Financial Derivatives, Neftci, S. N., Academic Press, 2000.
  • Value at risk: the new benchmark for controlling market risk, Jorion, P., McGrawHill, 2nd edition, 2001.
  • Mathematics for Finance, An introduction to financial engineering, Capinski, M., Zastawniak, T., Springer-Verlag, 2003.
  • Basic stochastic processes, Brzezniak, Z., Zastawniak, T., Springer-Verlag, 2006.
  • Introduction to mathematical finance, Pliska, S. R, Blackwell, 2006.
  • Financial risk manager handbook, second edition, Jorion, P., Wiley, 2003.
Διδακτικές και Μαθησιακές Μέθοδοι: 

Distance learningUse of ICT in teaching and communication with students

Μέθοδοι αξιολόγησης / βαθμολόγησης: 

Final exams in Greek (100%) which include open-ended questions, problem solving, written work.

Αντικειμενικοί Στόχοι μαθήματος (επιδιωκόμενα μαθησιακά αποτελέσματα): 
  • Understand and apply concepts from Probability and Statistics for financial data analysis and decision-making
  • Evaluate and manage financial risk
  • Understand the concept of stochastic processes and their application in modeling financial markets
  • Price options in both discrete and continuous time.

 

 

Περίγραμμα του Μαθήματος: 
PDF icon 5.FINANCIAL MATHEMATICS.pdf