Valuation and hedging of cryptocurrency inverse options

Currently, the most liquidly traded options on the crypto underlying are the so-called inverse options. An inverse option contract is quoted and traded in the units of the underlying cryptocurrency. The main economic reason for the popularity of inverse contracts in the crypto exchanges (such as Deribit) is that inverse contracts enable traders to operate without maintaining fiat cash accounts. For the theoretical part, we show that inverse options are just regular vanilla options considered under the martingale measure using the forward of the underlying as the numéraire. This measure requires an adjustment to option delta. For the empirical part, we use Deribit options data of past five years to backtest delta-hedged option strategies. We introduce USD and Coin accounting of trading Profit&Loss (P&L) which is important for designing strategies in crypto options. We show empirically that USD and Coin accounting rules are equivalent when performance is measured is Coin and USD units, respectively. We establish that the risk-premia observed in options on Deribit is negative and significant so that strategies selling volatility are expected to generate positive risk-adjusted performance in the long-term.