Detail práce

Monte Carlo Simulation of Swiss Franc LIBOR Using The Vasicek Model

Autor: Bc. Karel Kozmík
Rok: 2018 - letní
Vedoucí: prof. PhDr. Petr Teplý Ph.D.
Typ práce: Bakalářská
Jazyk: Anglicky
Stránky: 63
Abstrakt: We analyzed Swiss Franc LIBOR using R software and the Vasicek model. We utilized OLS, ML, bootstrap or simulations to test our hypotheses. The random walk hypothesis was not rejected, when we considered all the historical data. To get reasonable estimators, we used only data from the last adjustment of interest rates by the central bank and rejected the random walk hypothesis for all maturities but 12M. The difference in the results for OLS and ML estimates was negligible, so we did not reject the hypothesis that both methods give almost the same results. Performing a simulation study, we did not find any significant difference in the estimates for the Euler approximation for small values of the parameter a, but for larger values of a, the approximation led to biased results. All the hypotheses testing led the construction of confidence intervals for the estimated parameters, which are omitted in many papers and only point estimates are provided. We created confidence intervals for parameters of the Vasicek model for all the maturities but 12M. Extensive numerical simulations were run to explore the attributes of bootstrap estimates. We used an innovative approach of utilizing the logarithmic transformation to achieve a distribution closer to normal (which was necessary, because the intervals contained negative numbers and did not make sense), which to the best of our knowledge nobody used in this context.




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