Inverse and Quanto Inverse Options in a Black-Scholes World

TL;DR

This paper provides a mathematical analysis of inverse and quanto options in a Black-Scholes framework, comparing their pricing, hedging, and applications for fiat-based traders in crypto markets.

Contribution

It offers the first clear mathematical exposition of inverse and quanto options in crypto markets, analyzing their market incompleteness and practical applications.

Findings

Inverse and quanto options have distinct pricing and hedging characteristics.

Market incompleteness affects the valuation of crypto options.

Currency protected options offer practical benefits for fiat-based traders.

Abstract

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.