Module Handbook

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Module MAT-60-17-M-4

Probability Concepts for Financial Markets (M, 3.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-60-17-M-4 Probability Concepts for Financial Markets 3.0 CP (90 h)

Basedata

CP, Effort 3.0 CP = 90 h
Position of the semester 1 Sem. in WiSe/SuSe
Level [4] Bachelor (Specialization)
Language [EN] English
Module Manager
Lecturers
Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics
Livecycle-State [NORM] Active

Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2S MAT-60-17-K-4
Probability Concepts for Financial Markets
P 28 h 62 h
SEM-Schein
- no 3.0 WiSe/SuSe
  • About [MAT-60-17-K-4]: Title: "Probability Concepts for Financial Markets"; Presence-Time: 28 h; Self-Study: 62 h
  • About [MAT-60-17-K-4]: The study achievement [SEM-Schein] proof of successful participation in the seminar must be obtained.

Evaluation of grades

The module is not graded (only study achievements)..


Contents

  • Modelling of discrete-time financial markets,
  • Review and extensions of concepts from probability: Conditional expectation, martingales, stopping times, change of measure,
  • Binomial model,
  • Pricing of financial products in discrete-time financial markets,
  • European options,
  • American options,
  • Basics of portfolio optimization

Competencies / intended learning achievements

Upon completion of this module, students will be able to formulate and develop themodels ofdiscrete-time financial markets usingthe concepts of measure-theoretic probability theory. They will have learnt and processed the theory of discrete-time stochastic processes from probability theory and will be able to apply it to problems of financial mathematics. They will have acquired the fundamentals of price theory in discrete time financial markets and will be able to apply these methods to various types of financial derivatives.

By participating in the integrated seminar, students will have acquired additional skills useful for presenting mathematical content.

Literature

  • N.H. Bingham, R. Kiesel: Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives,
  • J. Jacod, P. Protter: Probability Essentials,
  • R. Korn: Moderne Finanzmathematik – Theorie und praktische Anwendung, Band 1: Optionsbewertung und Portfolio-Optimierung,
  • S. Pliska: Introduction to Mathematical Finance,
  • S. Shreve: Stochastic Calculus for Finance I: The Binomial Asset Pricing Model.

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-60-17-M-4]

Course of Study Section Choice/Obligation
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics Actuarial and Financial Mathematics [P] Compulsory