Financial Mathematics

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Module Title : Financial Mathematics

  • Type of Module:

PC (Prescribed Core Module)

x

PS (Prescribed Stream Module)

ES (Elective Stream Module)

E (Elective Module)

  • Level of Module

Postgraduate

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1st


  • Year of Study

1st


  • Semester

6


  • Number of credits allocated

  • Name of lecturer / lecturers : Georgios Mamanis and Nikolaos Thomaidis

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  • Description :

It is presented a wide range of mathematical theories and techniques that have been applied in finance. Specific sectors that are analyzed are investment appraisal, portfolio management, securities pricing and risk management.

  • Prerequisites:

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  • Module Contents ( Syllabus) :

Study unit 1st : Evaluation of fixed income securities

  • The basic theory of interest
  • Evaluation criteria: present value, future value, internal rate of return
  • Evaluation of bonds and other fixed income securities
  • Relation of interest rate and the price of fixed income securities

Study unit 2nd : Evaluation of single period random cash flows

  • Asset return and risk
  • The concept of portfolio of assets
  • Portfolio risk and return
  • The Markowitz model
  • The efficient frontier
  • The capital asset pricing model(CAPM)
  • The arbitrage pricing theory (APT)
  • Applications with real data

Study unit 3rd : Capital asset pricing based on arbitrage

  • Introduction to arbitrage
  • Stochastic models for the time evolution of capital asset prices
  • Replicating strategies (concept and design)
  • Option pricing: Binomial and Black-Scholes model

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  • Recommended Reading :

Α) Principal Reference :

  1. Βασιλείου Δ. και Ηρειώτης Ν. (2009) Ανάλυση επενδύσεων και διαχείριση χαρτοφυλακίου, Εκδόσεις Rosili.
  2. Luenberger D. G. (1997) Investment Science, OUP USA.
  3. Elton, E.J., Gruber, M.J., Brown, S.J., Goetzmann, W.N. (2007) Modern Portfolio Theory and Investment Analysis. 7th Edition, Wiley.

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Β) Additional References :

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  • Teaching Methods :

Lectures and exercises

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  • Assessment Methods :

The final grade will be based on:

  1. Final exams (70%)
  2. Homework (30%)

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  • Language of Instruction :

Greek

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  • Module Objective (preferably expressed in terms of learning outcomes and competences):

The course aims to introduce a wide range of mathematical theories and techniques that have been applied in finance. It is addressed to graduate students who want to understand the basic principles of mathematical finance and sectors like investment appraisal, portfolio management, securities pricing and risk management.