Most trading in cryptocurrency options is on inverse products, so called because the contract size is denominated in US dollars and they are margined and settled in crypto, typically bitcoin or ether. Their popularity stems from allowing professional traders in bitcoin or ether options to avoid transferring fiat currency to and from the exchanges. We derive new analytic pricing and hedging formulae for inverse options under the assumption that the underlying follows a geometric Brownian motion. The boundary conditions and hedge ratios exhibit relatively complex but very important new features which warrant further analysis and explanation. We also illustrate some inconsistencies, exhibited in time series of Deribit bitcoin option implied volatilities, which indicate that traders may be applying direct option hedging and valuation methods erroneously. This could be because they are unaware of the correct, inverse option characteristics which are derived in this paper.
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