Module Handbook

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Course MAT-61-11-K-7

Financial Mathematics (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in SuSe
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Additional informations
Livecycle-State [NORM] Active

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.

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.

Materials

Further literature will be announced in the lecture(s); exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-61-11-K-7]

Module Name Context
[MAT-61-11-M-7] Financial Mathematics P: Obligatory 4V+2U, 9.0 LP
[MAT-64-11A-M-7] Stochastic Differential Equations and Financial Mathematics P: Obligatory 4V+2U, 9.0 LP