| |
| Previous course: 04480 |
| Offered by:
Department of Mathematical Modelling
(IMM) |
| No credit points with: 04480 |
| Prerequisite: 04244/C0416 |
| Desirable: 04141/C0402 |
| Recommended semester:
7th - 9th semester |
| Scope and form: Lectures and tutorials. |
| Examination:
Written exam
(13 point scale
) |
| Remarks: Three mandatory problem sets should be handed in. They count for 40% of the final grade. |
| Contact person: |
Henrik Madsen, IMM, Building 321, Tel. +45 4525 3408 |
|
| Aim: The object is to enable the attendants to use statistical methods in mathematical finance. Emphasis is placed on estimation and inference in continuous time series. |
| Contents: Option theory: Risk-neutral valuation of put and call options in the Black and Scholes model. Arbitrage. Hedging. Interest rate derivatives. Linear and nonlinear time series analysis: ARCH models. Non-parametric methods. Stochastic differential equations: The Itô formula. Feynman-Kac representation theorems. Girsanov measure transformation. Discretization: Weak and strong convergence. Itô-Tayler series expansions. Simulation methods. Estimation theory: Maximum likelihood methods and method-of-moments (GMM). Kalman filtering. Bonds and the term structure of interest rates: Spot rate. Forward rate. Estimation of the term structure of interest rates. |
