Distribution of JPY/USD exchange rate returns

Tails in the distribution of JPY/USD exchange rate returns are well approximated by an exponentially dampened power-law. Distribution parameter estimates indicate that yen appreciation jumps belong to a Levy process with unbounded variation, suggesting that same mechanism may be responsible for fluctuations in normal times as well as rare crashes. In contrast, yen depreciation jumps have a well defined second moment suggesting a Gaussian regime. In addition, extreme episodes of yen appreciation are larger and more persistent than episodes of yen depreciation. The asymmetry is magnified and power-law tails are more elongated during times of higher interest rate differential between U.S. and Japan and higher level of VIX indicating that carry trade may be the driver. We propose a model of strategic carry trader behavior that in equilibrium generates exponentially dampened power-law distribution of jumps in foreign exchange along with “up by the stairs down by the elevator” dynamics arising from the assymetries between negative and positive jumps.

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