Pricing cryptocurrencies : Modelling the ETHBTC spot-quotient variation as a diffusion process

TL;DR

This paper models the intraday ETHBTC spot-quotient variation as an Ornstein-Uhlenbeck process, revealing mean-reversion and deviations from the theoretical no-arbitrage value over four years of data.

Contribution

It introduces a stochastic diffusion model for ETHBTC variation, demonstrating mean-reversion and quantifying deviations from no-arbitrage conditions.

Findings

Variation fluctuates around zero, not constantly zero.

Evidence of mean-reversion in the variation.

Long-term mean differs from zero at high precision.

Abstract

This research proposes a model for the intraday variation between the ETHBTC spot and the quotient of ETHUSDT and BTCUSDT traded on Binance. Under conditions of no-arbitrage, perfect accuracy and no microstructure effects, the variation must be equal to its theoretically computed value of 0. We conduct our research on 4 years of data. We find that the variation is not constantly 0. The variation shows a fluctuating behaviour on either side of 0. Furthermore, the deviations tend to be larger in the first year than the rest of the years. We test the sample for the nature of diffusion where we find evidence of mean-reversion. We model the variation using an Ornstein-Uhlenbeck process. A maximum likelihood estimation procedure is used. From the accuracy of the sampling distribution of the parameters obtained, we conclude that the variation may be accurately modelled as an Ornstein-Uhlenbeck process. From the parameters obtained, the long-term mean is shown to have a negative sign and differs from the theoretical value of 0 at 1e-05 precision. We take note of the results in light of efficiency of the markets to price publicly known information.