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Language: English |
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Previous course: 04480
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No credit points with: 04480
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Prerequisite: 04244
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Recommended semester: 7th - 9th semester
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Scope and form: Lectures and tutorials.
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Examination: Written exam.+ Three mandatory problem sets should be handed in. They count 40% of the final grade (13-scale)
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Department: Informatics and Mathematical Modelling
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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.
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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.
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