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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.

In this paper, we derive a representation for the value process associated to the solutions of FBSDEs in a jump-diffusion setting under multiple probability measures. Motivated by concrete financial problems, the latter representations are then applied to devise a generalization of the change of num\'eraire technique allowing to obtain recursive pricing formulas in the presence of multiple interest rates and collateralization., Comment: 25 pages. Minor typos removed

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.

In this paper we analyze the existence of cointegrating relationships between Bitcoin, S&P 500, and the quantity of money M2. We perform our analysis with and without applying time warping pre-processing. In all cases we find strong evidence that, in the period 2016-2021 the three time series show two cointegrating relationships and therefore share a common stochastic trend. In addition, a low correlation between Bitcoin and S&P 500 is detected. These finding justify the increased interest of investors in Bitcoin as an alternative asset class. The economic interpretation is that the stock valuation is primarily determined by financial phenomena, in particular the availability of large quantity of money. Money supporting investment is due both to the actions of Quantitative Easing and to the exchange of creditor/debtor role that took place between households and firms. The price of both Bitcoin and stocks is increasingly influenced by the amount of money in circulation and follows the same stochastic trend.

In this paper we test for regime changes and possible regime commonalities in the price dynamics of Bitcoin, Ethereum, Litecoin and Monero, as representatives of the cryptocurrencies asset class. Several parametric models are considered for the joint dynamics of the basket price where parameters are modulated through a Hidden Markov Chain with finite state space. Best specifications within Gaussian and Autoregressive models for price differences are selected by means of the AIC and BIC information criteria and through an out-of-sample forecasting performance. The empirical results, within the period January 2016 to October 2019, suggest that three or four states may be relevant to describe the dynamics of each individual cryptocurrency, depending on the selection criteria, while the entire basket displays at most three common states. Finally, we show how the identification of appropriate models may be exploited in order to build profitable investment strategies on the considered cryptocurrencies.

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.

Bitcoin is a digital currency traded on different exchanges for different prices; this feature implies important issues about arbitrage opportunities. In this paper we investigate whether strong or weak form of arbitrage strategies are indeed possible by trading across different Bitcoin Exchanges. Our investigation, both theoretically and practically, gives as a result that arbitrage is indeed possible.

This chapter illustrates a continuous time model for the dynamics of Bitcoin price, which depends on an attention or sentiment factor. The model is proven arbitrage-free under mild conditions and a quasi-closed pricing formula for European style derivatives is provided.

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.

Over the last decades, the natural disturbance is increasingly putting pressure on European forests. Shifts in disturbance regimes may compromise forest functioning and the continuous provisioning of ecosystem services to society, including their climate change mitigation potential. Although forests are central to many European policies, we lack the long-term empirical data needed for thoroughly understanding disturbance dynamics, modeling them, and developing adaptive management strategies. Here, we present a unique database of >170,000 records of ground-based natural disturbance observations in European forests from 1950 to 2019. Reported data confirm a significant increase in forest disturbance in 34 European countries, causing on an average of 43.8 million m3 of disturbed timber volume per year over the 70-year study period. This value is likely a conservative estimate due to under-reporting, especially of small-scale disturbances. We used machine learning techniques for assessing the magnitude of unreported disturbances, which are estimated to be between 8.6 and 18.3 million m3/year. In the last 20 years, disturbances on average accounted for 16% of the mean annual harvest in Europe. Wind was the most important disturbance agent over the study period (46% of total damage), followed by fire (24%) and bark beetles (17%). Bark beetle disturbance doubled its share of the total damage in the last 20 years. Forest disturbances can profoundly impact ecosystem services (e.g., climate change mitigation), affect regional forest resource provisioning and consequently disrupt long-term management planning objectives and timber markets. We conclude that adaptation to changing disturbance regimes must be placed at the core of the European forest management and policy debate. Furthermore, a coherent and homogeneous monitoring system of natural disturbances is urgently needed in Europe, to better observe and respond to the ongoing changes in forest disturbance regimes. Nasl. z nasl. zaslona. Opis vira z dne 12. 12. 2022. Skupno št. avtorjev: 24. Avtorja iz Slov.: G. Fidej, T. Nagel. Bibliografija: str. 1373-1376. Abstract.