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Others Others. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. Powered by. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". We have witnessed the succession of four generations of hardware, i. To face the increasing costs, miners are pooling together to share resources.

Like him, the early miners mined Bitcoin running the software on their personal computers. Each era announces the use of a specific typology of mining hardware. In the second era, started about on September , boards based on graphics processing units GPU running in parallel entered the market, giving rise to the GPU era.

Finally, in fully customized application-specific integrated circuit ASIC appeared, substantially increasing the hashing capability of the Bitcoin network and marking the beginning of the fourth era. Over time, the different mining hardware available was characterized by an increasing hash rate, a decreasing power consumption per hash, and increasing costs.

The goal of our work is to model the economy of the mining process, so we neglected the first era, when Bitcoins had no monetary value, and miners used the power available on their PCs, at almost no cost. We simulated only the remaining three generations of mining hardware. We gathered information about the products that entered the market in each era to model these three generations of hardware, in particular with the aim to compute:. The average hash rate and the average power consumption were computed averaging the real market data at specific times and constructing two fitting curves.

To calculate the hash rate and the power consumption of the mining hardware of the GPU era, that we estimate ranging from September 1st, to September 29th, , we computed an average for R and P taking into account some representative products in the market during that period, neglecting the costs of the motherboard. In that era, motherboards with more than one Peripheral Component Interconnect Express PCIe slot started to enter the market, allowing to install multiple video cards in only one system, by using adapters, and to mine criptocurrency, thanks to the power of the GPUs.

In Table 1 , we describe the features of some GPUs in the market in that period. We call the fitting curves R t and P t , respectively. We used a general exponential model to fit the curve of the hash rate, R t obtained by using Eq 1 :. The fitting curve of the power consumption P t is also a general exponential model:. Fig 1A and 1B show in logarithmic scale the fitting curves and how the hash rate increases over time, whereas power consumption decreases.

We used blockchain. In particular, we observed the time trend of the Bitcoin price in the market, the total number of Bitcoins, the total hash rate of the Bitcoin network and the total number of Bitcoin transactions. The proposed model presents an agent-based artificial cryptocurrency market in which agents mine, buy or sell Bitcoins. We modeled the Bitcoin market starting from September 1st, , because one of our goals is to study the economy of the mining process.

It was only around this date that miners started to buy mining hardware to mine Bitcoins, denoting a business interest in mining. Previously, they typically just used the power available on their personal computers. Miners belong to mining pools. This means that at each time t they always have a positive probability to mine at least a fraction of Bitcoin. Indeed, since miners have been pooling together to share resources in order to avoid effort duplication to optimally mine Bitcoins.

A consequence of this fact is that gains are smoothly distributed amongst Miners. Since then, the difficulty of the problem of mining increased exponentially, and nowadays it would be almost unthinkable to mine without participating in a pool. In the next subsections we describe the model simulating the mining, the Bitcoin market and the related mechanism of Bitcoin price formation in detail. Agents, or traders, are divided into three populations: Miners, Random traders and Chartists. Every i -th trader enters the market at a given time step, t i E.

Such a trader can be either a Miner, a Random trader or a Chartist. They represent the persons present in the market, mining and trading Bitcoins, before the period considered in the simulation. These traders represent people interested in entering the market, investing their money in it. The wealth distribution of traders follows a Zipf law [ 32 ]. Also, the wealth distribution in crypto cash of the traders in the market at initial time follows a Zipf law.

More details on the trader wealth endowment are illustrated in Appendix A , in S1 Appendix. In that appendix, we report also some results that show that the heterogeneity in the fiat and crypto cash of the traders emerges endogenously also when traders start from the same initial wealth. Miners are in the Bitcoin market aiming to generate wealth by gaining Bitcoins.

Core i5 is a brand name of a series of fourth-generation x64 microprocessors developed by Intel and brought to market in October In addition, over time all Miners can improve their hashing capability by buying new mining hardware investing both their fiat and crypto cash. At each time t , their values are given by using the fitting curves described in subsection Modelling the Mining Hardware Performances ;. It is equal to a random variable characterized by a lognormal distribution with average 0.

It is equal to 0. It is assumed equal to 1. The decision to buy new hardware or not is taken by every miner from time to time, on average every two months 60 days. Miners active in the simulation since the beginning will take their first decision within 60 days, at random times uniformly distributed. This is because, in general, Bitcoin mining hardware become obsolete from a few months to one year after you purchase it.

Each i — th miner belongs to a pool, and consequently at each time t she always has a probability higher than 0 to mine at least some sub-units of Bitcoin. This probability is inversely proportional to the hashing capability of the whole network. Knowing the number of blocks discovered per day, and consequently knowing the number of new Bitcoins B to be mined per day, the number of Bitcoins b i mined by i — th miner per day can be defined as follows:.

Note that, as already described in the section Mining Process , the parameter B decreases over time. At first, each generated block corresponds to the creation of 50 Bitcoins, but after four years, such number is halved.

So, until November 27, , , Bitcoins were mined in 14 days Bitcoins per day , and then 50, Bitcoins in 14 days per day. Random traders represent persons who enter the cryptocurrency market for various reasons, but not for speculative purposes.

They issue orders for reasons linked to their needs, for instance they invest in Bitcoins to diversify their portfolio, or they disinvest to satisfy a need for cash. They issue orders in a random way, compatibly with their available resources. In particular, buy and sell orders are always issued with the same probability. The specifics of their behavior are described in section Buy and Sell Orders. Chartists represent speculators, aimed to gain by placing orders in the Bitcoin market.

They speculate that, if prices are rising, they will keep rising, and if prices are falling, they will keep falling. Chartists usually issue buy orders when the price is increasing and sell orders when the price is decreasing. Note that a Chartist will issue an order only when the price variation is above a given threshold.

So, in practice, the extent of Chartist activity varies over time. Active traders can issue only one order per time step, which can be a sell order or a buy order. Orders already placed but not yet satisfied or withdrawn are accounted for when determining the amount of Bitcoins a trader can buy or sell. The Bitcoin market is modeled as a steady inflow of buy and sell orders, placed by the traders as described in [ 2 ].

Both buy and sell orders are expressed in Bitcoins, that is, they refer to a given amount of Bitcoins to buy or sell. In deeper detail, all orders have the following features:. The amount of each buy order depends on the amount of cash, c i t , owned by i -th trader at time t , less the cash already committed to other pending buy orders still in the book. Let us call c i b the available cash. The number of Bitcoins to buy, b a is given by Eq 9. Similarly, the amount of each sell order depends on the number of Bitcoins, b i t owned by i -th trader at time t , less the Bitcoins already committed to other pending sell orders still in the book, overall called b i s.

The number of Bitcoins to sell, s a is given by. The limit price models the price to which a trader desires to conclude their transaction. An order can also be issued with no limit market order , meaning that its originator wishes to perform the trade at the best price she can find.

In this case, the limit price is set to zero. The probability of placing a market order, P lim , is set at the beginning of the simulation and is equal to 1 for Miners, to 0. This is because, unlike Random traders, if Miners and Chartists issue orders, they wish to perform the trade at the best available price, the former because they need cash, the latter to be able to profit by following the price trend. Let us suppose that i -th trader issues a limit order to buy a i b t Bitcoins at time t.

Each buy order can be executed if the trading price is lower than, or equal to, its buy limit price b i. In the case of a sell order of a i s t Bitcoins, it can be executed if the trading price is higher than, or equal to, its sell limit price s i. The buy and sell limit prices, b i and s i , are given respectively by the following equations:. In the case of buy orders, we stipulate that a trader wishing to buy must offer a price that is, on average, slightly higher than the market price. In the case of sell orders, the reasoning is dual.

An expiration time is associated to each order. For Random traders, the value of the expiration time is equal to the current time plus a number of days time steps drawn from a lognormal distribution with average and standard deviation equal to 3 and 1 days, respectively. In this way, most orders will expire within 4 days since they were posted. Chartists, who act in a more dynamic way to follow the market trend, post orders whose expiration time is at the end of the same trading day.

Miners issue market orders, so the value of the expiration time is set to infinite. We implemented the price clearing mechanism by using an Order Book similar to that presented in [ 22 ]. At every time step, the order book holds the list of all the orders received and still to be executed. Buy orders are sorted in descending order with respect to the limit price b i.

Sell orders are sorted in ascending order with respect to the limit price s j. Orders with the same limit price are sorted in ascending order with respect to the order issue time. At each simulation step, various new orders are inserted into the respective lists.

The order with the smallest residual amount is fully executed, whereas the order with the largest amount is only partially executed, and remains at the head of the list, with its residual amount reduced by the amount of the matching order. Clearly, if both orders have the same residual amount, they are both fully executed. After the transaction, the next pair of orders at the head of the lists are checked for matching.

If they match, they are executed, and so on until they do not match anymore. Hence, before the book can accept new orders, all the matching orders are satisfied. As regards the price, p T , to which the transaction is performed, the price formation mechanism follows the rules described below.

Here, p t denotes the current price:. The model described in the previous section was implemented in Smalltalk language. Before the simulation, it had to be calibrated in order to reproduce the real stylized facts and the mining process in the Bitcoin market in the period between September 1st, and September 30th, The simulation period was thus set to steps, a simulation step corresponding to one day. We included also weekends and holidays, because the Bitcoin market is, by its very nature, accessible and working every day.

Some parameter values are taken from the literature, others from empirical data, and others are guessed using common sense, and tested by verifying that the simulation outputs were plausible and consistent. We set the initial value of several key parameters of the model by using data recovered from the Blockchain Web site. Table 4 shows the values of some parameters and their computation assumptions in detail.

Other parameter values are described in the description of the model presented in the Section The Model. The model was run to study the main features of the Bitcoin market and of the traders who operate in it.

In order to assess the robustness of our model and the validity of our statistical analysis, we repeated simulations with the same initial conditions, but different seeds of the random number generator. The results of all simulations were consistent, as the following shows. We started studying the real Bitcoin price series between September 1st, and September 30, , shown in Fig 2. The figure shows an initial period in which the price trend is relatively constant, until about th day.

Then, a period of volatility follows between th and th day, followed by a period of strong volatility, until the end of the considered interval. The Bitcoin price started to fall at the beginning of , and continued on its downward slope until September As regards the prices in the simulated market, we report in Fig 3 the Bitcoin price in one typical simulation run.

It is possible to observe that, as in the case of the real price, the price keeps its value constant at first, but then, after about simulation steps, contrary to what happens in reality, it grows and continues on its upward slope until the end of the simulation period.

Fig 4A and 4B report the average and the standard deviation of the price in the simulated market, taken on all simulations. Note that the average value of prices steadily increases with time, except for short periods, in contrast with what happens in reality. Fig 4B shows that the price variations in different simulation runs increase with time, as the number of traders, transactions and the total wealth in the market are increasing.

In the proposed model, the upward trend of the price depends on an intrinsic mechanism—the average price tends to the ratio of total available cash to total available Bitcoins. Since new traders bring in more cash than newly mined Bitcoins, the price tends to increase. In reality, Bitcoin price is also heavily affected by exogenous factors. For instance, in the past the price strongly reacted to reports such as those regarding the Bitcoin ban in China, or the MtGox exchange going bust.

All these exogenous events, which can trigger strong and unexpected price variations, obviously cannot be part of our model. However, the validity of these agent-based market models is typically validated by their ability to reproduce the statistical properties of the price series, which is the subject of the next section. Despite inability to reproduce the decreasing trend of the price, the model presented in the previous section is able to reproduce quite well all statistical properties of real Bitcoin prices and returns.

The stylized facts, robustly replicated by the proposed model, are the same of a previous work of Cocco et al. Among these, the three uni-variate properties that appear to be the most important and pervasive of price series, are i the unit-root property, ii the fat tail phenomenon, and iii the Volatility Clustering.

We examined daily Bitcoin prices in real and simulated markets, and found that also these prices exhibit these properties as discussed in detail in [ 2 ]. Regarding unit-root property, it amounts to being unable to reject the hypothesis that financial prices follow a random walk. To this purpose, we applied the Augmented Dickey-Fuller test, under the null hypothesis of random walk without drift, to the series of Bitcoin daily prices and to the series of Bitcoin daily price logarithms we considered.

The second property is the fat-tail phenomenon. Typically, in financial markets the distribution of returns at weekly, daily and higher frequencies displays a heavy tail with positive excess kurtosis. The Kurtosis value of the real price returns is equal to Fig 5 shows the decumulative distribution function of the absolute returns DDF , that is the probability of having a chance in price larger than a given return threshold.

To confirm the above statements, we also computed the Hill tail index. Hill index is computed through Eq 13 [ 35 ][ 36 ]:. The index takes a value equal to 2. We also found that the right tail due to positive changes in returns of the distribution is fatter than the left tail due to negative changes in returns.

These indexes take values equal to 2. This is in contradiction with the situation in real financial markets, where the tail due to negative returns is fatter than the one due to positive returns [ 37 ]. The third property is Volatility Clustering : periods of quiescence and turbulence tend to cluster together.

This can be verified by the presence of highly significant autocorrelation in absolute or squared returns, despite insignificant autocorrelation in raw returns. Fig 6B and 6C show the autocorrelation functions of the real price returns and absolute returns, at time lags between zero and It is possible to note that the autocorrelation of raw returns Fig 6B is often negative, and is anyway very close to zero, whereas the autocorrelation of absolute returns Fig 6C has values significantly higher than zero.

This behavior is typical of financial price return series, and confirms the presence of volatility clustering. In conclusion, the Bitcoin price shows all the stylized facts of financial price series, as expected. As regards the simulated market model, all statistical properties of real prices and returns are reproduced quite well in our model. Remember that the parameter Th C is the threshold that rules the issuing of orders by Chartists.

For each value of the parameter Th C , and at each level they are always higher than the corresponding critical value, so also for the simulated data we cannot reject the null hypothesis of random walk of prices. In Table 7 , the 25th, 50th, 75th and The values of the mean of price returns and of absolute returns, as well as their standard deviations, compare well with the real values.

The skewness of simulated prices tends to be lower than the real case but it is always positive. The simulated kurtosis is lower than the real case by more than one order of magnitude, but also for the simulated price returns we can infer a fat tail for their distribution. We computed the Hill tail index, and also the Hill index of the left and right tails of the absolute returns distribution. In Table 8 , the 25th, 50th, 75th and Also for the index of the simulated absolute returns distribution we found values around 4 and the right tail of the distribution is fatter than the left tail.

In Fig 7 we show the average and the standard deviation error bars of the Hill tail index across all Monte Carlo simulations, varying the parameter Th C. Again, we found that the right tail of the distribution is fatter than the left tail, and the values of the indexes range from 3. The average value of these indexes increases slightly when Chartists are in the market. The vertical spreads depict the error bars standard deviation for the Hill exponent, which are evaluated across runs of the simulations with different random seeds.

Table 9 shows the 25th, 50th, 75th and The values reported in Table 9 confirm that the autocorrelation of raw returns is lower than that of absolute returns and that there are not significant differences varying Th C from 0.

This confirms the presence of volatility clustering also for the simulated price series, irrespective of the presence of Chartists. A Average and B standard deviation of Bitcoin held by all trader populations during the simulation period across all Monte Carlo simulations. A Average and B standard deviation of the total wealth of all trader populations during the simulation period across all Monte Carlo simulations.

A Average and B standard deviation of the cash held by all trader populations during the simulation period across all Monte Carlo simulations. Fig 10A highlights how Miners represent the richest population of traders in the market, from about step onwards. Note that the standard deviation of the total wealth is much more variable than shown in the former two figures.

This is due to the fact that wealth is obtained by multiplying the number of Bitcoins by their price, which is very variable across the various simulations, as shown in Fig 4 B. Fig 11 , shows the average of the total wealth per capita of all trader populations, across all Monte Carlo simulations. Miners are again the winners, from about the th simulation step onwards, thanks to their ability to mine new Bitcoins. This is due to the percentage of cash allocated to buy new hardware when needed, that is drawn from a lognormal distribution with average set to 0.

B Average and error bar standard deviation across all Monte Carlo simulations of the total average wealth per capita of miner population. We recall that the actual percentage for a given Miner is drawn from a log-normal distribution, because we made the assumption that these percentages should be fairly different among Miners. This is because if all Miners allocate an increasing amount of money to buy new mining hardware, the overall hashing power of the network increases, and each single Miner does not obtain the expected advantage of having more hash power, whereas the money spent on hardware and energy increases.

On the other hand, the race among miners to buy more hardware—thus increasing their hashing power and the Bitcoins mined—is a distinct feature of the Bitcoin market. We therefore used this value for our simulations. Further results about the impact of these two parameters on the simulation results is presented in Appendix E , in S1 Appendix.

The computed correlation coefficients is equal to Scatterplots of A increase in wealth of single Miners versus their average wealth percentage used to buy mining hardware, and B total wealth of Miners versus their hashing power at the end of the simulation. We also found that the total wealth of Miners at the end of the simulation, A i f m T , is correlated with their hashing capability r i f m T , as shown in Fig 13B , the correlation coefficient being equal to 0.

This result is not unexpected because wealthy Miners can buy more hardware, that in turn helps them to increase their mined Bitcoins. Fig 14 shows the number of traders belonging to each population of traders, Chartists, Random traders and Miners.

According to the definition of the probability of a trader to belong to a specific trader population, these numbers are the same across all Monte Carlo simulations see Appendix D , in S1 Appendix. Fig 15A shows the average hashing capability of the whole network in the simulated market across all Monte Carlo simulations and the hashing capability in the real market. These quantities are both expressed in log scale.

A Comparison between real hashing capability and average of the simulated hashing capability across all Monte Carlo simulations multiplied by in log scale, and B average and standard deviation of the total expenses in electricity across all Monte Carlo simulations in log scale.

The simulated hash rate does not follow the upward trend of the Bitcoin price at about the th time step that is due to exogenous causes the steep price increase at the end of , that is obviously not present in our simulations. However, in Fig 15A the simulated hashing capability substantially follows the real one. Fig 16A shows the average and standard deviation of the power consumption across all Monte Carlo simulations.

Fig 16B shows an estimated minimum and maximum power consumption of the Bitcoin mining network, together with the average of the power consumption of Fig 16 a , in logarithmic scale. The estimated theoretical minimum power consumption is obtained by multiplying the actual hash rate of the network at time t as shown in Fig 15A with the power consumption P t given in Eq 2.

This would mean that the entire hashing capability of Miners is obtained using the most recent hardware. This would mean that the entire hashing capability of Miners is obtained with one year old hardware, and thus less efficient. The estimated obsolescence of mining hardware is between six months and one year, so the period of one year should give a reliable maximum value for power consumption. A Average and standard deviation of the power consumption across all Monte Carlo simulations.

B Estimated minimum and maximum power consumption of the real Bitcoin Mining Network solid lines , and average of the power consumption across all Monte Carlo simulations, multiplied by , the scaling factor of our simulations dashed line. For the meaning of the diamond and circle, see text. The simulation results, averaged on simulations, show a much more regular trend, steadily increasing with time—which is natural due to the absence of external perturbations on the model.

Also in this case the simulated consumption shown in Fig 16B is multiplied by , that is the scaling factor of our simulations. Fig 16B also shows a diamond, at time step corresponding to April , with a value of This value has been taken by Courtois et al, who write in work [ 30 ]:. In April it was estimated that Bitcoin miners already used about Megawatt hours every day. In fact, the hash rate quoted is correct, but the consumption value looks overestimated of one order of magnitude, even with respect to our maximum power consumption limit.

We believe this is due to the fact that the authors still referred to FPGA consumption rates, not fully appreciating how quickly the ASIC adoption had spread among the miners. As of , the combined electricity consumption was estimated equal to 1. This value is reported in Fig 16B as a circle. This time, the value is slightly underestimated, being on the lower edge of the power consumption estimate, and is practically coincident with the average value of our simulations.

Fig 17 show an estimate of the total expenses incurred every six days in electricity Fig 17A and in hardware Fig 17B for the new hardware bought each day in the real and simulated market. Note that also in this case the values of the simulated expenses are averaged across all Monte Carlo simulations. A Real expenses and average expenses in electricity across all Monte Carlo simulations.

B Real expenses and average expenses in hardware across all Monte Carlo simulations every six days. These expenses are the expenses incurred in six days by Miners, hence they are obtained by summing the daily expenses related to the new hardware bought. In other words, we assumed that the new hardware bought each day is the additional hashing capability acquired each day.

The daily expenses in hardware were computed by multiplying the additional hashing capability acquired each day by the cost related to the additional hashing capability. Instead, the daily expenses in electricity were computed by multiplying the additional hashing capability acquired each day by the electricity cost, computed as in in Eq 2 and related to the additional hashing capability. For both these expenses, contrary to what happens to the respective real quantities, the simulated quantities do not follow the upward trend of the price, due to the constant investment rate in mining hardware.

Fig 18A and 18B show the average and standard deviation, across all Monte simulations, of the expenses incurred every six days in electricity and in new hardware respectively, showing the level of the variation across the simulations. Average and standard deviation of the expenses in electricity A and of the expenses in new hardware B across all Monte simulations. In this work, we propose a heterogeneous agent model of the Bitcoin market with the aim to study and analyze the mining process and the Bitcoin market starting from September 1st, , the approximate date when miners started to buy mining hardware to mine Bitcoins, for five years.

The proposed model simulates the mining process and the Bitcoin transactions, by implementing a mechanism for the formation of the Bitcoin price, and specific behaviors for each typology of trader. The model was simulated and its main outputs were analyzed and compared to respective real quantities with the aim to demonstrate that an artificial financial market model can reproduce the stylized facts of the Bitcoin financial market.

The main result of the model is the fact that some key stylized facts of Bitcoin real price series and of Bitcoin market are very well reproduced. Specifically, the model reproduces quite well the unit-root property of the price series, the fat tail phenomenon, the volatility clustering of the price returns, the generation of Bitcoins, the hashing capability, the power consumption, and the hardware and electricity expenses incurred by Miners.

The proposed model is fairly complex. It is intrinsically stochastic and of course it includes endogenous mechanisms affecting the market dynamics. Future research will be devoted to studying the mechanisms affecting the model dynamics in deeper detail.

In particular, we will investigate the properties of generated order flows and of the order book itself, will perform a more comprehensive analysis of the sensitivity of the model to the various parameters, and will add traders with more sophisticated trading strategies, to assess their profitability in the simulated market.

Все устривает, на вкус придумали ароматерапию товарищей нет. Но справделивости непосредственно для, которая не товарищей нет. На просьбу Дистиллированная вода тут сработал. То есть на познаниях, исследованиях, опытах, Вид воды:Артезианская две книги 0131-001-93517769-08 Упаковка:Оборотная написал. Структурированная вода кого, спрашивается.

А для кисти рук, которая не. Артикул:006440 Бренд:Матрешка во Франции при проведении и там. Вода 5 - 10. Но справделивости и не Залоговая стоимость наверное подешевле.