Financial markets are chaotic. So chaotic, even, that many economists and investors believe market trends to be the product of ‘random walks’ and that prices cannot be predicted (see generally Malkiel). But randomness shouldn't be worrisome. In fact, random price movements can be good. Gaussian random walk, an assumption used by an options pricing model called Black-Scholes, treats intervals of an asset’s price over time as independent variables. By doing so, the changes in price over time, or the returns of an asset, are assumed to be normally distributed. Otherwise stated, “If transactions are fairly uniformly spread across time, and if the number of transactions per day, week, or month is very large, then the Central Limit Theorem leads us to expect that these price changes will have normal or Gaussian distributions” (Fama, 399). When an asset's returns are normally distributed, the probabilities of those returns are known. Knowing these probabilities can give investors a reliable framework accounting for the risk of holding said asset. When it comes to bitcoin, much has been said about how risky it is. The purpose of this article is to explore how to frame risk and to test how well traditional assumptions, implicit in derivatives pricing, apply to bitcoin.

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