Poisson process Models of extreme volatility of Bitcoin prices

• 1、School of Mathematics and Information Sciences,Yantai University

Abstract：In recent years, digital currencies based on blockchain technology have received widespread attention from global investors and financial regulatory agencies, and the dramatic fluctuations of their price are the major conerns. Previous studies on asset price fluctuations mainly focused on traditional capital markets such as stocks and bonds, while there are less research on price fluctuations in the emerging digital currency market i.e. the Bitcoin. Bitcoin is a currency with intrinsic value that is difficult to quantify, produced entirely by computer computing power, and has no endorsement from any national government or financial institution as a financial asset. Therefore, as a financial asset, the Bitcoin prices often experience violent fluctuations due to numerous complex factors. In this study, two Poission process models, non-homogeneous Poisson process (NHPP) model and the fractional Poisson process (FPP) model, are used to fit the violent Bitcoin price volatility sequence. The NHPP model generalizes the intensity λ of the Poisson process to a function λ(t), reflecting the non-stationarity of violent Bitcoin price fluctuation events. The fractional Poisson process is also a generalization of the homogeneous Poisson process model, where the time interval distribution is extended from the exponential distribution to the Mittag-Leffler distribution. The fractional Poisson process reflects long-term memory effects. In this study, two Poisson point process models are applied to the event sequence of sharp fluctuations in the price of Bitcoin through estimating model parameters and graphical evaluation model fitting, and the ocurruing of the next is aslo predicted and analyzed.

keywords： Volatility Bitcoin price nonhomogeneous Poisson process Peak-over-Threshold Continuous Time Random Exceedances Fractional Poisson process

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