Module Handbook

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Module MAT-61-11-M-7

Financial Mathematics (M, 9.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-61-11-M-7 Financial Mathematics 9.0 CP (270 h)

Basedata

CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in SuSe
Level [7] Master (Advanced)
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.
4V+2U MAT-61-11-K-7
Financial Mathematics
P 84 h 186 h - - PL1 9.0 SuSe
  • About [MAT-61-11-K-7]: Title: "Financial Mathematics"; Presence-Time: 84 h; Self-Study: 186 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86200 ("Financial Mathematics")

Evaluation of grades

The grade of the module examination is also the module grade.


Contents

  • Basics of stochastic analysis (Brownian motion, Itô integral, Itô formula, martingale representation theorem, Girsanov theorem, linear stochastic differential equations, Feynman-Kac formula),
  • Diffusion model for stock prices and trading strategies,
  • Completeness of market,
  • Option pricing with the replication principle, Black-Scholes formula
  • Option pricing and partial differential equations,
  • Exotic Options,
  • Arbitrage bounds (Put-Call parity, parity of prices for European and American calls),
  • Outlook on portfolio optimization.

Competencies / intended learning achievements

Upon successful completion of the module, students understand the basic structures and properties of stochastic integrals and stochastic differential equations and they are familiar with the Itô formula and Girsanov's theorem. They are exposed to various models of financial market, including the Black Scholes model, to understand the different methods for the pricing of financial derivatives. They can critically assess the limits of modelling and the applicability of methods to different financial derivatives.

By completing the exercises, students have developed a skilled, precise and independent handling of the terms, propositions and methods taught in the course. They understand the proofs presented in the lecture and are able to reproduce and explain them. They can in particular outline the conditions and assumptions that are necessary for the validity of the statements and how these are to be interpreted in the context of actuarial and financial mathematics.

Literature

  • N.H. Bingham, R. Kiesel: Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives,
  • T. Björk: Arbitrage Theory in Continuous Time,
  • I. Karatzas, S.E. Shreve: Brownian Motion and Stochastic Calculus,
  • I. Karatzas, S.E. Shreve: Methods of Mathematical Finance,
  • R. Korn, E. Korn: Option Pricing and Portfolio Optimization – Modern Methods of Financial Mathematics.

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Module / Module Number [MAT-61-11-M-7]

Course of Study Section Choice/Obligation
[MAT-88.B84-SG] M.Sc. Actuarial and Financial Mathematics Actuarial and Financial Mathematics [P] Compulsory
Module-Pool Name
[MAT-61-MPOOL-7] Specialisation Financial Mathematics (M.Sc.)
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)