Will the price of bitcoin reach 100,000 dollars this year? Someone used the Monte Carlo method to predict

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[AI Technology Camp Guide] Science and technology blogger Xoel López Barata is trying to use a simple Monte Carlo simulation method to predict the daily income of Bitcoin, and trying to predict the end of this year, the price of bitcoin is most likely to reach. He also published a source code, link: Https://github.com/xoelop/Misc

Before discussing this statistical method, the original Bo like thunder a disclaimer: This forecast is purely fun, does not represent Bitcoin investment advice. If you want to invest, please do a full investigation, do not blindly, causing unnecessary losses. In addition, the future earnings of Bitcoin are not necessarily a significant growth trend, and the past performance does not represent the future price performance.



Don't worry, it's an adventure that takes only 5 minutes.

▌ What is the daily income.

The benefit is defined as the price difference between an observation value and its next observation. In this case, because we are looking at the daily data, the corresponding income will also be the daily income.

The easiest way to calculate daily income:



Ideally, the day-to-day benefits of financial assets should be normal.

But that is not the case. The actual daily rate of return "tail" is more hypertrophy. This means that the probability of extreme events is higher than the normal distribution prediction, and the distribution is different, as shown in the figure:



You can hardly tell the difference between two distribution tails in the above picture, but the distribution of the proceeds will be much fatter.

▌ What is Monte Carlo simulation.

The Monte Carlo method (or the Montessori Experiment) is a widely used computational algorithm that relies on repeated random sampling to obtain numerical results.

When using the Monte Carlo simulation method to predict the price of money, we assume that the future behavior of asset prices is similar to that of the past, and we randomly generate many future behavioral versions similar to the past-random walk (random walks). This completes the process of extracting random samples from past behavior and stacking them together to create each random walk.



Assuming that the future will be similar to the past is a bold assumption, it may not be true, but we currently have only these data

▌ using Monte Carlo method to forecast 2018 BTC/USD Price

To build each random walk in the simulation process, we randomly sampled the daily earnings data from 2010 to date, adding 1 to each sample and accumulating until December 31, 2018. The price of the current bitcoin is then multiplied by the value of the random walk to obtain the simulated bitcoin future price. This will be repeated many times (100,000 times in this case), and by the end of this year we will see the final price distribution for each random walk.

▌ Random Walk

The first 200 random walks look like this:



100,000 linear graphs of 200 in Random walk

The graph provides a limited amount of information because the exponential growth of some random walks makes the Y-scale of the graph larger, and most random walks end with a random walk in blue. Here, changing the longitudinal axis to a logarithmic scale will help us see things that are easier to observe:



Logarithmic graph of 200 random walks shown earlier

▌ Final Price distribution

We can see that most random walks of the outcome price between 10,000 dollars to 100,000 dollars.

But just according to the graphic results above, we can't get more information. Now from the histogram below we can see the distribution of the final price of all 100,000 random walks that we have previously generated. As shown in the figure:



We are faced with the same problem again and we cannot draw any conclusions from this drawing. The workaround is the same as before: use logarithmic coordinates to draw data on the horizontal axis. In this way, the diagram looks much better:



The final price that looks most likely from the diagram is between $24K and $90K.

In order to find the price more accurately, I have a few other options. One is to simply calculate the median value of the final price distribution: 58843 dollars. The other is to estimate the probability density function by the kernel density estimation method and find the price corresponding to the maximum value of the function.

The results are shown in the following illustration:



As you can see, the most likely final price estimates are similar, all above $5,0000.

It is noteworthy that this estimate is not necessarily the final result, but it can be better used to find the confidence intervals for future final prices. In this case, the bitcoin price 80% confidence interval will be between 13,200 and 271,277 dollars. Another way to look at this is that the chances of a price below 13,200 per cent by the end of the year are the same as the price of more than 271,277 dollars (if the price is the same in the future).

What else is there?

Now we have the KDE density function, for example, we can calculate the probability that the end price will be below a certain level.

If we want to calculate the probability that the price is equal to or below January 20, 2018, we simply integrate the shaded area into the following figure:



What is the probability value? 9.84%.



His parting words were "I never thought that the probability is so low." ”

▌ Recommendations

There is a theorem: Nothing can ever rise, the past and the future are not converging. Here is the trend chart for the U.S. base currency over the years. It also rose a lot.



The base currency is the most active part of the U.S. money supply. It includes bills, coins and bank deposits.

And you, do you believe that America can keep printing money forever?

Therefore, the future earnings of Bitcoin will not necessarily resemble the previous earnings trend; And the performance of past prices is not indicative of future prices.

In this respect, the battalion commander reiterated: investment is risky, buy currency to be cautious.

Author | Xoel López Barata

Original text | https://medium.com/@xoelop/WEVE-SIMULATED-THE-BITCOIN-PRICE-FOR-THE-WHOLE-2018-YOU-WON-T-BELIEVE-THE-RESULT-4A602679DAC2

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