Aplikace náhodných procesů ve financích
Applications of stochastic processes in finance
diploma thesis (DEFENDED)
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http://hdl.handle.net/20.500.11956/17284Identifiers
Study Information System: 45982
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- Kvalifikační práce [10932]
Author
Advisor
Consultant
Karlova, Andrea
Referee
Dostál, Petr
Faculty / Institute
Faculty of Mathematics and Physics
Discipline
Probability, mathematical statistics and econometrics
Department
Department of Probability and Mathematical Statistics
Date of defense
16. 9. 2008
Publisher
Univerzita Karlova, Matematicko-fyzikální fakultaLanguage
Czech
Grade
Excellent
In this thesis we consider a stochastic volatility model based on non-Gaussian Ornstein-Uhlenbeck process (see also Barndor -Nielsen and Shephard [1]) where the logarithm of an asset price is the solution of a stochastic di erential equation without drift. The volatility component is modelled as a stationary, latent Ornstein-Uhlenbeck process, driven by a non-Gaussian Lévy process. We perform Bayesian inference for model parameters by means of Markov chain Monte Carlo algorithm based on data augmentation. The algorithm corresponds to a standard hierarchical parametrization of the model. The aim of this thesis is to express the unobserved stochastic volatility process for observed asset price. The algorithm is applied to the simulated and real asset price where real asset price is US dollar (USD) - Pound sterling (GBP) exchange rate.