Abstract
We derive the Bitcoin exchange rate dynamics by solving the exchange rate equation of the standard flexible-price monetary model to investigate any characteristics of Bitcoin like a currency. The dynamics is driven by an asymmetric mean-reverting fundamental shock which can be attributed to a money demand shock. A crash occurs when the exchange rate with a weakened mean-reverting force breaches a lower boundary where a smooth-pasting condition is imposed. The empirical results show the exchange rate dynamics can be calibrated according to the model, in which the mean reversion of the dynamics is positively co-integrated with the Bitcoin transaction volume indicating demand for Bitcoin; and with the risk reversals of the commodity currencies (Australian dollar and Canadian dollar) in currency option markets. The analysis shows that the Bitcoin exchange rate shares some characteristics of commodity currencies with crash risk. This suggests that Bitcoin behaves as a currency between fiat money and a crypto-commodity used for trading and investment purposes.
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