Vorlesung im Sommersemester 2014:
Numerische Methoden der Finanzmathematik 1
Computational Finance 1
Gliederung
10.04.2014
§ 1. Modelling Tools for Financial Options
16.04.2014
1.1 Options
- Example 1: FX Risk Management at Apple (iPhone Production)
17.04.2014
1.2 Model of the Financial Market
- Example 2: Pricing of a structured product
23.04.2014
1.3 The Binomial Method
24.04.2014
30.04.2014
1.4 Risk-Neutral Valuation
07.05.2014
1.5 Stochastic Processes
08.05.2014
1.6 Stochastic Differential Equations
- Definition 1: Itô Stochastic Differential Equation
- Algorithm 1: Euler-Maruyama discretization
- Example 1:
- geometric Brownian Motion (GBM)
- Risk-Neutral Valuation
- Implied Volatility
- Market Price of Risk
- Mean Reversion
- Vasicek model, CIR model, square root process
14.05.2014
1.7 Itô's Lemma and Applications
15.05.2014
1.8 Jump Models
1.9 Calibration
21.05.2014
§ 2. Generating Random Numbers with Specified Distributions
2.1 Uniform Deviates
22.05.2014
2.2 Extension to Random Variables from Other Distributions
2.3 Normally Distributed Random Variables
28.05.2014
§ 3. Monte Carlo Simulations with Stochastic Differential Equations
3.1 Approximation Error
3.2 Stochastic Taylor Expansion
04.06.2014
3.3 Numerical Methods
05.06.2014
3.4 Intermediate Values
3.5 Monte Carlo Simulation
18.06.2014
3.5 Monte Carlo Methods for American Options
25.06.2014
§ 4. Additional topics
4.1 Pricing Basket Options using the Mellin Transform
26.06.2014
4.2 Nonlinear Black-Scholes equations
02.07.2014
4.3 Modelling Stochastic Correlation
03.07.2014
4.4 Pricing of Weather and Energy Derivatives
09.07.2014
4.5 The Quasi Monte Carlo Method
10.07.2014
4.6 Principal Component Analysis in Finance
16.07.2014
4.7 An Adjoint method for fast computing of Monte Carlo Greeks
17.07.2014
4.8 Discussion of Oral Exam
