Price discovery in fiat currency and cryptocurrency markets

•Thispaperinvestigatesthe linkage of direct exchange rate of fiat currencies and the rate implied by bitcoin(BTC)prices by investigating the relative contributions of actual and implied exchange rates to price discovery.•The BTC-implied ratescontribute more to price discovery than actual rates forEUR/USD, GBP/USD, and JPY/USD.•The triangular arbitrage opportunitiesbetween actual and implied ratesare related to the market capitalization of BTC and the futures trading in Chicago Board Options Exchange (CBOE) and Chicago Mercantile Exchange & Chicago Board of Trade (CME). We study the dynamic relations between the direct exchange rate of fiat currencies and the rate implied by bitcoin prices. The empirical results show the deviation between actual and implied rates of EUR/USD, GBP/USD, and JPY/USD affects the movements of actual and BTC-implied rates. We observe that implied rates contribute more to price discovery than actual rates before 2019 for EUR/USD and before 2018 for JPY/USD. Triangular arbitrage opportunities arise when VIX is high. The arbitrage opportunities are also related to the market capitalization of bitcoin and the trading of bitcoin futures on CBOE and CME.