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In this paper, we apply dynamic factor analysis to model the joint behaviour of Bitcoin, Ethereum, Litecoin and Monero, as a representative basket of the cryptocurrencies asset class. The empirical results suggest that the basket price is suitably described by a model with two dynamic factors. More precisely, we detect one integrated and one stationary factor until the end of August 2019 and two integrated factors afterwards. Based on this evidence, we define a multiple long-short trading strategy which proves profitable when the second factor is stationary.

The goal of this paper is to provide a novel quantitative framework to describe the Bitcoin price behavior, estimate model parameters and study the pricing problem for Bitcoin derivatives. To this end, we propose a continuous time model for Bitcoin price motivated by the findings in recent literature on Bitcoin, showing that price changes are affected by sentiment and attention of investors, see e.g., (Kristoufek in Sci Rep 3:3415, 2013, PLoS ONE 10(4):e0123923, 2015; Bukovina and Marticek in Sentiment and bitcoin volatility. Technical report, Mendel University in Brno, Faculty of Business and Economics 2016). Economic studies, such as Yermack (Handbook of Digital Currency, chapter second. Elsevier, Amsterdam, pp 31–43, 2015), have also classified Bitcoin as a speculative asset rather than a currency due to its high volatility. Building on these outcomes, the price dynamics in our suggestion is indeed affected by an exogenous factor which represents market attention in the Bitcoin system. We prove the model to be arbitrage-free under a mild condition and we fit the model to historical data for the Bitcoin price; after obtaining a approximate formula for the likelihood, parameter values are estimated by means of the profile likelihood method. In addition, we derive a closed pricing formula for European-style derivatives on Bitcoin, the performance of which is assessed on a panel of market prices for Plain Vanilla options quoted on www.deribit.com .

In this paper, we analyze the relative impact of attention measures either on the mean or on the variance of Bitcoin returns by fitting nonlinear econometric models to historical data: Two non-overlapping subsamples are considered from January 1, 2012, to December 31, 2017. Outcomes confirm that market attention has an impact on Bitcoin returns and volatility, when measured by applying several transformations on time series for the trading volume or the SVI Google searches index. Specifically, best candidate models are selected via the so-called Box–Jenkins methodology and by maximizing out-of-sample forecasting performance. Overall, we can conclude that trading volume-related measures affect both the mean and the volatility of the cryptocurrency returns, while Internet searches volume mainly affects the volatility. An interesting side finding is that the inclusion of attention measures in model specification makes forecast estimates more accurate.

Bitcoin is a digital currency started in early 2009 by its inventor under the pseudonym of Satoshi Nakamoto. In the last few years, Bitcoin has received much attention and has shown a surprising price increase. Bitcoin is currently traded on many web-exchanges making it a rare example of a good for which different prices are readily available; this feature implies important issues about arbitrage opportunities since prices on different exchanges are shown to be driven by the same risk factor. In this paper, we show that simple strategies of strong arbitrage arise by trading across different Bitcoin exchanges taking advantage of the common risk factor. The suggested arbitrage strategies are based on two alternative model specifications. Precisely, we consider the multivariate versions of Black and Scholes model and of an attention-based dynamics recently introduced in the literature.

The curse of dimensionality problem refers to a set of troubles arising when dealing with huge amount of data as happens, e.g., applying standard numerical methods to solve partial differential equations related to financial modeling. To overcome the latter issue, we propose a Deep Learning approach to efficiently approximate nonlinear functions characterizing financial models in a high dimension. In particular, we consider solving the Black–Scholes–Barenblatt non-linear stochastic differential equation via a forward-backward neural network, also calibrating the related stochastic volatility model when dealing with European options. The obtained results exhibit accurate approximations of the implied volatility surface. Specifically, our method seems to significantly reduce the neural network’s training time and the approximation error on the test set.

In this paper we test for regime changes in the price dynamics of Bitcoin, Ethereum, Litecoin and Monero, as representatives of the cryptocurrencies asset class. Data are observed daily from January, 1, 2016 to October, 15, 2019. Best specifications within Gaussian and Autoregressive Hidden Markov models for price differences are selected through the AIC and BIC information criteria by considering up to four hidden regimes. The empirical results suggest that at most three common states may be considered for the basket of cryptocurrencies under investigation; a fourth state may be relevant as an added factor to the dynamics description of the individual cryptocurrencies rather than to the whole basket. Finally, we test the out-of-sample performance of estimated regime switching models; optimal results, in terms of RMSE and correlation between predicted and real values, are obtained in the case of two common or three individual regimes.

In this paper we measure market attention by applying several filters on time series for the trading volume or the SVI Google searches index. We analyze relative impact of these measures either on the mean or on the variance of Bitcoin returns by fitting non linear econometric models to historical data from January 1, 2012 to October 31, 2017; two non-overlapping subsamples are also considered. Outcomes confirm our conjecture that market attention has an impact on Bitcoin returns. Specifically, trading volume related measures affect both the mean and the conditional variance of Bitcoin returns while internet searches volume mainly affects the conditional variance of returns.

In recent literature it is claimed that BitCoin price behaves more likely to a volatile stock asset than a currency and that changes in its price are influenced by sentiment about the BitCoin system itself; in Kristoufek the author analyses transaction based as well as popularity based potential drivers of the BitCoin price finding positive evidence. Here, we endorse this finding and consider a bivariate model in continuous time to describe the price dynamics of one BitCoin as well as a second factor, affecting the price itself, which represents a sentiment indicator. We prove that the suggested model is arbitrage-free under a mild condition and, based on risk-neutral evaluation, we obtain a closed formula to approximate the price of European style derivatives on the BitCoin. By applying the same approximation technique to the joint likelihood of a discrete sample of the bivariate process, we are also able to fit the model to market data. This is done by using both the Volume and the number of Google searches as possible proxies for the sentiment factor. Further, the performance of the pricing formula is assessed on a sample of market option prices obtained by the Deribit website.