**Disclaimer: This is written for fun; it’s just assumptions of the author and not investment advice. Do your own analysis, do not do stupid things and do not keep in cryptocurrency funds more than you can afford to lose.**

However, the author believes that bitcoin is hard money, while Fiat currency is not. Therefore, if you believe that hard and uncensored money is important for a sufficiently large number of people, then this can cause future results to resemble the past until the majority of the population realizes that bitcoin is the best money.

So, since you’re already interested in the title and are here, let’s play with some numbers.

## Don’t Worry, it Will be an Adventure for Just 5 Minutes

I have built a simple model using Monte Carlo for a daily increase in the dollar price of bitcoins to find out what will be his most probable price at the end of 2018 was Used for this code can be found on my GitHub.

### Daily gain? What’s it?

An increase is an indicator of price change between two observations. In this case, we consider the data by day and, accordingly, daily gain. And how is it calculated? There are several forms. Enough to be very simple:

In an ideal world daily net acquisition of financial assets follows a normal distribution, but this is far from reality, and the real growth rate has thicker tails. What’s the meaning of that? This means that extreme events occur with a higher probability than the normal distribution, and the distribution is different, as can be seen below.

### The Growth of Bitcoin and the Normal Distribution

It is impossible to see the difference in tails, but believe me, the distribution of growth they are thicker.

### But What is the Monte Carlo Model?

According to Wikipedia, Monte Carlo methods (or Monte Carlo experiments) are a wide class of computational algorithms that use repeated random samples to produce numerical results.

In fact, when building financial models Monte-Carlo simulation assumes that the future price behavior of an asset will remind her past behavior, and generate many random versions of this similar to the past of the future, called random walks.

### Model Monte Carlo Rates: BTC/USD in 2018

To construct random walks for our model, we will take random samples of the daily increment from 2010 to the present day, add one to each and multiply them sequentially until December 31, 2018. After that, we multiply the current bitcoin price by the random walk values to get the future price model. This will be done many times (in this case 100,000) and at the end of the year we will see the distribution of the final price for each random walk.

### Random Walk

The first 200 random walks are as follows:

This graph gives us little information since the exponential growth of some random walks increased y of the graph, whereas most random walks turned out to be much lower than the blue random walk. The logarithmic scale for the vertical axis will help us better see what’s going on:

### The Distribution of the Final Price

As you can see, the final price in most of the random walks is between $10 thousand and $100 thousand in the above schedule, we have little to say beyond this. It would be nice to see a histogram of the distribution of the final prices of all 100,000 generated by us previously random walks. Here it is:

**Distribution of simulated prices as at 31 December 2018**

**Distribution of simulated prices as at 31 December 2018**

We face the same challenge as above, and we cannot draw any conclusions from that timetable. The solution is the same: use the logarithmic scale for the horizontal axis. So the schedule looks much better:

**Density / Price ( $ ) (logarithmic scale)**

It seems most probable price ranges from $24 thousand to $90 thousand to More accurately determine the price in several ways. One is simply to calculate the 50th percentile of the final price distribution: $ 58,843. Another is to calculate the probability density function using the nuclear density estimate and find the price corresponding to the maximum of this function. The result is shown below:

**The distribution of simulated prices of bitcoin on December 31, 2018**

Density / Price ( $ ) (logarithmic scale)

**Peak: the Most probable price: $55530**

Yellow — a Function of kernel estimators of the density

Blue — End of the modelled price

As you can see, the most probable price estimates are similar and both are above $ 50 thousand.

It is important to note that this assessment should not be taken literally, and it is better to use it to determine the confidence intervals of the future distribution. In this case, the confidence interval of the bitcoin price with a probability of 80% is between $13,200 and $271,277. In another way, we can say that the probability that the price at the end of the year will be below $13,200 is the same as that it will be above $271,277 (if the price movement in the future will resemble its movement in the past).

### What Else?

Since we now have a function of nuclear density estimation, we can, for example, calculate the probability that the price at the end of the year will be below a certain level.

In particular, if we want to calculate the probability that the price will not be higher than today (January 20, 2018) , we just need to integrate the shaded area on the following chart:

**The distribution of simulated prices of bitcoin on December 31, 2018**

Density / Price ( $ ) (logarithmic scale)

Mark: the Current price

**And what is the probability? Of 9.84%.**

**Bonus** tip

Yeah, I know. Nothing can last forever, and if something was in the past, it does not mean that it will be in the future. Below is a graph of something else, which is also in the past has grown greatly.

The adjusted monetary base, Federal reserve Bank of St. Louis

**Billion dollars**

The shaded area indicates U.S. recession

Source: Federal reserve Bank of St. Louis

The monetary base – the most liquid part of money supply of the United States. It includes banknotes, coins and Bank deposits.

**How much do you believe the US will be able to continue to extract money from the air forever?**

If you intend to seriously and believe in the growth of Bitcoin, we advise you Cloud Mining Service – HashFlare.io

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