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Approximation of Evacuation Curve by the Polynomic Regression Method
Uhlík, Ondřej ; Dobiášová, Lucie ; Kratochvílová, Martina
Prediction of the evacuation process at the time of the emergency is crucial for the subsequent effective coordination of the evacuation and the intervention of the rescue units. Microscopic simulation tools are currently the most advanced method of evacuation modelling, however, their use in the operational phase of construction is inefficient due to the computational time of the simulations and dynamic input data. One of the outputs of the simulations is the evacuation curve. The paper proposes a simplification of the curve by the approximation method of polynomial regression, which demonstrates on basic evacuation scenario. The polynomial coefficients can be used to compile a training set of a machine learning model to predict real-time evacuation curves.
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Estimation of risk-neutral probability density functions from option prices
Krejčí, Kateřina ; Málek, Jiří (advisor) ; Diviš, Martin (referee)
The thesis deals with the estimation of risk-neutral probability density functions from option prices. It focuses on smoothing techniques that are applied to volatility smile. Theoretical part describes the estimation principle and presents some solutions for problems that occur while estimating the risk-neutral distribution. The findings from the theoretical part are used in the practical part and applied to real data. An analysis of the influence of the selection of particular smoothing function on the final distribution is performed. At the end of the thesis a stability test of estimations is performed and the analysis of dynamics of risk neutral distribution is shown on a small data sample.
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