Stochastic Models

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Stochastic Models
Course ID: 
Course Description: 
Track course
Financial Engineering

The course includes an introduction in probability theory. Αdditionally, it deals with interest rates and present value analysis. Financial market and derivatives are also presented along with capital pricing under the efficient markets hypothesis. Actually the latter introduces stochastic analysis (martingales) in modeling the dynamics of financial measures.


Module Contents (Syllabus)



  • Equities, Bonds, Stock Market
  • Financial Derivatives
  • Types of Traders (Hedgers, Speculators Arbitrageurs), Investment Strategies (Bull spread, Bear spread, Butterfly Spread, Straddle, Strip and Strap, Strangles)
  • Simple, Discount, Compound interest, Present Value Analysis
  • Forwards and Futures pricing
  • Option pricing and Hedging – One-period Binomial Model
  • Risk neutral Probability Measure
  • σ-algebra, Measure, , Stochastically Independent Events, Conditional Expectation , Stochastic Process
  • Martingales
  • Dynamic Portfolio, Self-financing Portfolio in discrete time, Mutliperiod Binomial Model, No-arbitrage pricing in Mutliperiod Binomial Model
  • Brownian Motion, Geometric Brownian Motion
  • Black-Scholes Formula
  • Applications of Black-Scholes Formula



Class schedule: 
Wednesday 09.00-12.00, Classroom A ΝΑΜΕ
Assessment methods: 

Final Exams 100%

Recommended Reading:

Α) Principal Reference:


  1. Στοχαστικά χρηματοοικονομικά, Βασιλείου Π. – Χ., Εκδόσεις ΖΗΤΗ, 1η έκδοση, 2001. (in greek)
  2. Στοιχειώδης εισαγωγή στα χρηματοοικονομικά μαθηματικά, Ross S., ΕΚΔΟΣΕΙΣ ΠΑΝΕΠΙΣΤΗΜΙΟΥ ΜΑΚΕΔΟΝΙΑΣ, 1η έκδοση, 2007. (in greek)


Β) Additional References:


  1. An Elementary Introduction to Mathematical Finance: Options and other Topics, Ross, S., Cambridge University Press; 2nd edition , 2002.
  2. Options, Futures and Other Derivatives, Ηull, J., 5th edition, Prentice Hall, 2003.
  3. The Mathematics of Financial Derivatives, Willmott, P., Howison, S., Dewynne, J., Cambridge University Press. .1997.
  4. An Introduction to the Mathematics of Financial Derivatives, Neftci, S. N., Academic Press, 2000.