## Price of Bitcoin for 2018

On January 22, user Medium Joel Lopez Barata published a post: “I calculated the price of bitcoin for the entire year 2018. You will not believe the result! “With the disclaimer” this is just an opinion, not an investment council. ” Lopez’s mathematical calculations are based on the hypothesis that the behavior of bitcoin in the future will correspond to his behavior in the past. In this case, Lopez considers bitcoin “healthy money”, and Fiat – no: “The future profit will be equal to the last, while most people understand that bitcoin is the best money.”

The Lopez simulation is based on the Monte Carlo method. This is a wide range of computational algorithms that rely on repeated random samples. In this case, Lopez uses the daily dollar profit from bitcoin to understand what the approximate price will be by the end of 2018.

To calculate the daily profit, he divides the current bitcoin price by the price for the last day and subtracts the unit: “Speaking about Monte Carlo simulation in finance, we assume that the future price behavior of the asset will be similar to its past behavior, and create a lot of random versions of this future , which is known in mathematics as “random walks”. The full code for creating such a simulation is available on GitHub.

To build each random walk model in the simulation, one must take random samples of daily profit from 2010 to today, add them and then multiply cumulatively until December 31, 2018. After that, the current price of bitcoin is multiplied by the value of a random walk, and the result is a simulation of the future price. This needs to be done many times (in this case – 100,000 times), and at the end of the year we will see the final price distribution for each random walk.

#### The first 200 of 100,000 random walks look like this:

It turns out that the final price for most random walks ranges from $ 10,000 to $ 100,000. The following diagram shows the distribution of final prices for all 100,000 random walks:

It shows that the most likely price varies between $ 24,000 and $ 90,000. To understand it more precisely, there are several ways. First, you can simply calculate the 50% -th percentile of the distribution of final prices. It will be equal to $ 58,843. Another method is to calculate the probability density function using the nuclear density estimate and find the price corresponding to the maximum of this function – $ 55,530.

But this is not the final indicator, it is still better to use it to find the confidence interval. For the bitcoin price, the 80% confidence interval will be $ 13,200 – $ 271,277. He also points out that the chances that by the end of the year the price will be below $ 13,200 are the same as the chances that it will be above $ 271,277.

Now that the nuclear density estimate is known, it is possible to calculate the probability that the cost of bitcoin will fall by the end of the year relative to a certain indicator. In particular, the probability that the price will be lower or equal to the level of January 20 ($ 12,000), is 9.84%.

*Author: Richard Abermann *

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