Calibtating tempered stable Levy models to data of cryptocurrencies Bitcoin and Ethereum
Abstract
Calibtating tempered stable Levy models to data of cryptocurrencies Bitcoin and Ethereum
Incoming article date: 28.11.2019In the paper, we consider the problem of modeling the dynamics of leading cryptocurrencies such as Bitcoin (BTC) and Etherium (ETH). We calculate the log-returns based on the time series of cryptocurrency rates and analyze the realized power variation to estimate the corresponding generalized Blumenthal-Getoor index. The analysis shows that tempered stable Levy processes without a diffusion component are suitable for modeling the cryptocurrency rates considered. To obtain a more accurate estimate of the parameter that describes the activity of jumps in the log-returns, we exclude the influence of drift by considering auxilary series of increments of the initial log-returns.
Keywords: mathematical modeling, cryptocurrencies, Levy models, Tempered Stable Levy models, CGMY modes, Blumenthal-Getoor index, realized power variation