Part 1. General problems of the intellectual systems theory

Jump diffusion model with mean-reverting lognormal volatility

R. V. Chestnov<sup>ab

a</sup> Qset
^b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Currently, there are numerous stochastic models built for different market concepts. However, almost all of these models are based and tested for traditional markets, while at present the cryptoasset market is gaining tremendous momentum in terms of volume and market capitalisation. For this reason, the idea arises to create such a model, which would be built specifically for the cryptoasset market, taking into account all its peculiarities and behavioural patterns. In this paper, we will try to look at some of the features that are noticeable for cryptoassets and build a stochastic model that takes them into account, and after that, we will compare it with another model that is similar in structure. It is notable right away that, similar to how traditional models are used for cryptomarkets, our model for cryptoassets will interpret the traditional market just as well. Moreover, even better than in the opposite case, because the main idea of our model is to take into account various critical events that occur with this or that asset, but by calibrating the model in the right way, we can ignore them.

Keywords: Financial mathematics, stochastic calculus, cryptoas-sets, neural networks, Feynman-Kac equation, Bates model, likelihood function