Nonlinear dynamics of Kimchi premium

Abstract

Kimchi premium, the persistent non-zero price difference exists between the US and Korean crypto-markets. Not only does the premium represent a violation of the law of one price but it may also reflect the bubble aspect of crypto-markets or crypto-market segmentation. Contrary to the literature relying on linear modelling, we employ threshold regression with multiple regimes to show the nonlinear dynamics of the premium and identify its determinants. We find that the premium is mean-reverting when it exceeds a certain level of thresholds but displays a random walk inside the range, which implies that only for relatively large-sized premiums, arbitrageurs exploit the premium. Kimchi premium has a non-zero long run steady-state level of 1.24% for Bitcoin aligned with the violation of the law of one price. We demonstrate that the non-zero premium exists due in part to market frictions given that the trading fee is positively correlated with the threshold.