Cryptocurrency Volatility Risk

Consider the scenario of person A in the US sending a payment to person B in Europe. Person A could buy cryptocurrency XYZ using USD, send the cryptocurrency to person B who could then sell XYZ for EUR. The risk here is that the exchange rate for cryptocurrency XYZ moves significantly while person B awaits confirmation of the payment on the cryptocurrency blockchain. Another example is when one uses a cryptocurrency as an intermediary to purchase a different cryptocurrency, e.g. USD to BTC to XEM since the XEM/USD trading pair does not exist.

We define the volatility risk as the volatility of an asset multiplied by the time it takes for the asset to settle. This metric will allow us to distinguish between holding a high volatility asset for a short amount of time and holding a low volatility asset for a large amout of time. The time it takes for a transaction to settle for several cryptocurrencies is given in the following table:
Cryptocurrency \(n_c\) \(t_b\)
BTC 6 35 Min.
XRP 1 3.5 Sec.
ETH 30 14 Sec.
LTC 12 2.5 Min.
XMR 15 2 Min.
where \(n_c\) represents the typical number of confirmations required [1] and \(t_b\) the time to generate a block. We define the volatility risk as \[\sigma_{in} = \frac{\sigma}{365^{1/2}} (\delta t)^{1/2},\]where \(\sigma\) denotes the 90-day annualized volatility of the cryptocurrency and \(\delta t = n_c t_b\) denotes the time it takes for the transaction in units of days. The lower the volatility risk, the more attractive a cryptocurrency is as an intermediary. For example, let \(X(t=0)\) denote a cryptocurrency exchange rate before use as an intermediary. After being used as an intermediary the value at time \(X(t=\delta t)\) will lie between \[ X(0)(1-3 \sigma_{in}/100) \leq X(\delta t) \leq X(0)(1+3 \sigma_{in}/100) \] 99.7% of the time. For example, consider the volatility risk for Bitcoin trading at \(X(t=0) = BTC/USD = $20,000 \) and \(\sigma_{in} = 1\), then after settlement \( $19,400 \leq X(\delta t) \leq $20,600 \). This chart is in logscale and updated daily.

BTC = Bitcoin, XRP = Ripple, ETH = Ethereum, LTC = Litecoin, XMR = Monero.

Raw price data courtesy of Poloniex.
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