Calibtating tempered stable Levy models to quotes of cryptocurrencies
Abstract
Calibtating tempered stable Levy models to quotes of cryptocurrencies
Incoming article date: 13.12.2020In this article, we consider the problem of modeling the dynamics of cryptocurrencies using a wide class of tempered stable Levy processes. At the first step, the generalized Blumenthal-Getour index is estimated based on the realized power-law variation of a number of logarithmic returns of cryptocurrency rates. We consider the case when the jump activity index is less than one, which corresponds to Levy processes of bounded variation. The modeled process is then presented as a sequence of positive and negative Levy jumps over short periods of time. We calibrate the model to one-touch artificial digital options, which are the statistical probabilities of crossing predetermined barriers, and we suggest using the FFT in conjunction with the Wiener-Hopf method. The main advantage of our approach is the use of explicit Wiener-Hopf factorization formulas to determine the price of one-touch synthetic digital options within such models. The proposed technique simplifies the fitting of parameters of non-Gaussian Levy processes with jump activity not exceeding 1. In essence, we replace the original continuous-time process with a discrete process that approximates a tempered stable Levy process.
Keywords: mathematical modeling, cryptocurrencies, Levy models, Tempered Stable Levy models, CGMY modes, Blumenthal-Getoor index, options