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Title: Heavy-tailed stochastic models with time-dependent coefficients: Applications to financial time series Authors:  Agnieszka Wylomanska - Wroclaw University of Science and Technology (Poland) [presenting]
Abstract: To properly manage market risk, industrial companies use tools based on value-at-risk, which requires proper modeling of future risk factors dynamics. One of the major challenges faced by this technique applied to modeling financial time series is the choice of an appropriate model for the simulation of the future paths. In order to fit the data, it should reflect its properties including heavier than Gaussian tail distributions, stabilizing volatility and mean reversion in long term horizon. We propose to apply the extension of the classical stochastic model with fixed coefficients for the description of currency exchange rates data and the metals prices. This model was introduced for describing the evolution of the short interest rate and could be considered as the natural extension of the classical Ornstein-Uhlenbeck process, where the coefficients are constant. The standard version of the model was based on the Brownian motion (BM). However, it can be easily extended to any class of distributions. Since the financial data of interest exhibit non-Gaussian behavior, we modify the model to use skewed generalized Students $t$-distribution. We demonstrate the estimation techniques and present the real-life applications to financial time series.