Financial Mathematics I

Information about the course

  • Financial market models in discrete time: arbitrage freeness and completeness     
  • Conditional expectation and discrete time martingales
  • Valuation of European, American and path-dependent options
  • Foundations of continuous time market models and of the Black-Scholes model
  • Interest rate models and derivatives
  • Risk measures
  • Portfolio optimisation and CAPM

This course covers the fundamental principles and techniques of financial mathematics in discrete- and continuous-time models. Specific topics are

Type and Prerequisites

  • Type
    • Bachelor Mathematische Biometrie (optional)
    • Bachelor/Master Mathematik (optional)
    • Bachelor/Master Wirtschaftsmathematik (optional)
    • Master Wirtschaftswissenschaften (optional)
    • Master of Finance-Major Financial Mathematics (obligatory)
    • Master of Finance-Major Financial Economics (obligatory)
    • Master of Finance-Major Actuarial Science (obligatory)
  • Prerequisites
    • Analysis I+II
    • Lineare Algebra I+II
    • Stochastik I 
    • Elementary Probability, Statistics
    • Measure Theory or Introduction to Measure Theoretic Probability (can be attended in the same winter term)

Exam & DAV-Certificate

  • There will be a closed written exam after the end of the course (closed means you need to take the first exam to be allowed to take the retake of the exam)
  • Date: to be announced
  • There will be a retake exam at the end of the semester break
  • Date: to be announced
  • The exam for the DAV certificate will be right after the first exam
  • Note that there will only one DAV exam, so there is no DAV exam after the retake exam

Time and Venue

Financial Mathematics 1 is a (4+2)-course and there will be 4 hours of lecture and 2 hours of exercise every week.

  • Lecture: Tuesday 14:15-15:45 in N24 H12 and Thursday 12:15-13:45 in N24 H12
  • Exercise Classes: Thursday: 8:15-9:45 HeHo18 E20, Friday: 8:15-9:45 HeHo18 E20, 10:15-11:45 O28 2004 and N24 H12 and 14:15-15:45 HeHo 18 1.20

Lecture Notes and Exercises

All materials will be available on Moodle.

The students must attend one of the exercise classes. The exact allocation will be done in moodle in the first week of the semester. At the begining the exercise classes the students can state which exercises they solved. After that for each exercise a random student will be asked to present his solution. Please bring your student ID to the exercise classes in order to avoid any possibility of identity confusion. Overall, the students must solve 50% of the exercises in order to be admitted to the exam (to achieve the "Vorleistung").



Robert Stelzer

Class teacher

Bennet Ströh


  • On Friday, 18.10.2019 from 10:15-11:45 there will be a repetition of the concept of conditional expectation 
  • Date of the first lecture: Tuesday, 15.10.2019 14:15-15:45
  • The exercise classes begin in the second week of the semester


  • Baxter, M.; Rennie, A.: Financial Calculus: An introduction to derivative pricing. (Cambridge University Press), 1996.
  • N.H.Bingham & R.Kiesel, Risk Neutral Valuation (2nd edition), Springer 2004.
  • Björk, T.: Arbitrage theory in continuous time. (Oxford University Press,
    Oxford) 2.edn. 2003.
  • H. Föllmer & A. Schied, Stochastic Finance: An introduction in discrete time, de Gruyter, 2004.
  • Korn, R.; Korn, E.: Option Pricing and Portfolio Optimization. (American Mathematical Society, Providence), 2001.
  • Musiela, M.; M. Rutkowski: Martingale methods in financial modelling. (Springer, New York), 2nd ed. 2004.
  • S. Shreve, Stochastic Calculus for Finance I: The  Binomial Asset Pricing Model, Springer, 2004.
  • S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.