Financial Mathematics (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||9.0 CP||186 h|
|2||U||Exercise class (in small groups)||28 h|
|(4V+2U)||9.0 CP||84 h||186 h|
- 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.
- 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.
Further literature will be announced in the lecture(s); exercise material is provided.
Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-60-11-M-4] Probability Theory (M, 9.0 LP)
Requirements for attendance (formal)