# What will be the price bitcoin in 2018 — simulation of Monte Carlo (forecast)

The beginning of 2018 for bitcoin was to put it mildly not really, and on January 17 the price of the first-ever cryptocurrency has fallen up to \$9511. Earlier, I already wrote about the reflections concerning why the price for bitcoin has fallen, in the same article I will tell about recently carried out simulation of Monte Carlo which predicts the movement of a course bitcoin in 2018. At once I want to emphasize that this simulation has been carried out in the fact-finding purposes, and 100% can’t be the forecast of the price bitcoin. You won’t find anywhere the forecast which will surely come true, nobody knows precisely as couple of BTC/USD in the future will behave.

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The Monte Carlo method — the generalized name of group of numerical methods which are based on receiving a large number of realization of the stochastic (casual) process formed so that his probabilistic characteristics coincided with similar sizes of a solvable task.

On January 22, the user by the name of Xoel López Barata, has published interesting simulation by the Monte Carlo method, based on day return.
Day return = (the price/price for previous day)-1.

In ideally taken world, day return from financial assets will be distributed evenly, however the reality is far from an ideal because in practice daily income has more dense tails. It means that extreme events (divergences) have higher probability, unlike the predicted distribution therefore such distributions aren’t similar at each other that can be noticed below.

Simulation of Monte Carlo in the field of finance assumes that in the future the behavior of the price of an asset will be like his behavior in the past therefore the set of the casual versions of this future called by «random walks» (random walks) is generated. It becomes by means of the casual examples of behavior from the past put with the same samples for creation of random walk.

Important

As it was already possible to understand, there is no guarantee that future income will be similar to previous; the previous movement of the price isn’t the exact indicator of the price in the future. Therefore once again I remind that the carried-out simulation is only indicative.

BUT, as the price not of some fiatny currency, but bitcoin is predicted, most likely the ascending tendency as still a huge number of people don’t use this cryptocurrency will remain.
Simulation of the price of BTC/USD for 2018

To construct each random walk in this simulation, random selection of the previous day returns of bitcoin which is added to each of samples and is multiplied cumulatively till December 31, 2018 undertakes. After that we multiply the current price of Bitcoin of value of each random walk to receive simulation of the price in the future. In the presented simulation it has been made 100000 times.

Final distribution of the prices

The histogram which shows final distribution of the prices for bitcoin from all 100000 casual walks is given below. It is possible to notice that their main weight is in a limit from \$10000 to \$100000:

It seems that the most probable price bitcoin is between \$24000 and \$90000, but more precisely to determine this price, it is possible to choose one of the following options:

It is simple to find 50% of distribution of the final prices — \$58843.
To estimate function of density of distribution of a kernel (Kernel Density Estimation) and to find the price corresponding to a maximum of this function.

It is important to note once again that you shouldn’t take this figure too seriously. She can be used to find an approximate interval of future distribution of the price. At this simulation, there are 80% of probability that the price of BTC will be in a limit from \$13200 to \$271277.

Also it is worth taking in attention that probability that the price at the end of 2018 will be higher than 271277 dollars, just the same, as the probability of the price is lower than 13200 dollars (if the price moves in the future also, as well as in the past).

What else?

As we have a function of density of KDE, it is possible to calculate probability that at the end of 2018 the rate of bitcoin will be below a certain level. If we want to calculate probability that the price will be equal or lower than \$12951 (the price of the moment of carrying out simulation).

This probability is 9.84%. 