15000 - Financial Mathematics in Discrete Time Modulübersicht

Module Number: 15000
Module Title:Financial Mathematics in Discrete Time
  Finanzmathematik in diskreter Zeit
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Wunderlich, Ralf
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
Learning Outcome:

After successful completion of the module, students have gained in-depth knowledge from the Probability Theory module and are able to apply it. They are familiar with the key concepts involved in modeling time-discrete stochastic financial markets and have mastered basic methods for valuing and hedging derivatives. In addition, students gained experience in independent academic work through the study of topics in financial mathematics.

Contents:
  • Basic concepts of financial markets
  • Discrete-Time stochastic processes and martingales
  • Mathematical modeling of time-discrete financial markets
  • One- and multi-period model, binomial model, transition to the Black Scholes model
  • Pricing and hedging of derivatives
  • Portfolio optimization
Recommended Prerequisites:

Knowledge of the content of module 

  • 11217: Wahrscheinlichkeitstheorie
Mandatory Prerequisites:

No successful participation in module 11345 Finanzmathematik I

Forms of Teaching and Proportion:
  • Lecture / 3 Hours per Week per Semester
  • Exercise / 1 Hours per Week per Semester
  • Self organised studies / 180 Hours
Teaching Materials and Literature:
  • Föllmer, Schied: Stochastic Finance, de Gruyter, 2004
  • Pliska: Introduction to Mathematical Finance, Blackwell, 1997
  • Shreve: Stochastic Calculus for Finance I, Springer, 2004
Module Examination:Final Module Examination (MAP)
Assessment Mode for Module Examination:
  • Written examination, 90 min. OR
  • Oral examination, 30 min. (with small number of participants)

In the first lecture it will introduced, whether the examination will organized in written or oral form.

Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Master (research-oriented) / Mathematical Data Science / PO 2025
  • Master (research-oriented) / Mathematics / PO 2025
Remarks:
  • Study programme Mathematics M.Sc.: Compulsory elective module in the module complex „Stochastics”
  • Study programme Mathematical Data Science M.Sc.: Compulsory elective module in the module complex „Advanced Mathematical Methods in Data Science”
Module Components:
  • Lecture: Financial Mathematics in Discrete Time
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester:
  • no assignment