Bitcoin analysis - Monte Carlo Simulation Method [15/02 to 15/03]

Last month has been a ride for cryptocurrency investors. Bitcoin has followed a down trend with a minimum closing point of 7051,57USD, until it bounced back on track hitting recently 10.000USD mark - were talking about a 6784,35USD range between High and Low within a month: huge!

Content list:

1. Past performance analysis - data analytics, VaR, average profitability
2. Monte Carlo Simulation - Geometric Brownian Motion
3. Data inference and forecast

Past performance analysis

Note: there is a formatting error concerning the horizontal axis values. P(X=0) refers to the interval [-0.05:0] and so on.

According to the data retrieved from 31 days we can state with 95% accuracy that the average bitcoin value was in between 10244,74+-663,63USD. The distribution graph had a slightly positive skewness which means the average returns were concentrated in negative values.

The historical VaR - Value at Risk was -15%, which means that if you invested X dollars, you would be 95% confident that your worst daily loss would be 0.15% of your initial investment.

Monte Carlo Simulation - GBM forecast and prediction

"A Monte Carlo simulation applies a selected model (that specifies the behavior of an instrument) to a large set of random trials in an attempt to produce a plausible set of possible future outcomes. In regard to simulating stock prices, the most common model is geometric Brownian motion (GBM). GBM assumes that a constant drift is accompanied by random shocks."

Read more: Monte Carlo Simulation With GBM https://www.investopedia.com/articles/07/montecarlo.asp#ixzz57Jft6EPN

Essentially previous month data was taken with cyclical and irrelevant variables being stripped out to establish the foundations to this forecast.

There were made about 500 iterations to decrease associated error. Prices are normally distributed and price variation is log-normally distributed respecting the price compound effect.

So, as we can see the estimated VaR for the next 30 days period is -20%. Although the average return rate will return to positive territories, it still remains a huge downward pressure.

Note: Notice the limitations of the model, it's based on inference. It does not take into consideration sudden unexpected trend changes nor price jumps but surely it gives you an idea at the very least of probable future market performance.

Any question or critics are appreciated!
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