  Over 90% of exchange trading on crypto options has always been on the Deribit
platform. This centralised crypto exchange only lists inverse products because
they do not accept fiat currency. Currently, fiat-based traders can only make
deposits in bitcoin, although they can withdraw both bitcoin and ether to their
on-chain wallets. Likewise, other major crypto options platforms only list
crypto--stablecoin trading pairs in so-called direct options, which are similar
to the standard crypto options listed by the CME except the U.S. dollar is
replaced by a stablecoin version. Until now a clear mathematical exposition of
these products has been lacking. We discuss the sources of market
incompleteness in direct and inverse options and compare their pricing and
hedging characteristics. Then we discuss the useful applications of currency
protected "quanto" direct and inverse options for fiat-based traders and
describe their pricing and hedging characteristics, all in the Black-Scholes
setting.
