Delta hedging bitcoin options with a smile

We analyse robust dynamic delta hedging of bitcoin options using a set of smile-implied and other smile-adjusted deltas that are either model-free, in the sense that they are the same for every scale-invariant stochastic and/or local volatility model, or they are based on simple regime-dependent parameterisations of local volatility. These deltas are popular with option market makers in traditional assets because they are very easy to implement. Previous empirical research on dynamic delta hedging is based solely on equity index options, but we have a unique data set of hourly historical bitcoin option prices between January 2020 and January 2022. We show that about 85\% of trading activity is on options with expiry less than four weeks, and hence we focus on those options in this study. For call and put options with a wide range of moneyness and with synthetic constant maturities of 10, 20 and 30 days we compare the dynamic hedging performance of these different deltas over two one-year periods. We also analyse the use of the perpetual contract rather than the standard futures as hedging instrument and results are presented as testable statistics of hedging error variance ratios. In certain periods the use of smile-implied hedge ratios can significantly out-perform the simple Black-Scholes delta hedge, especially when using the perpetual swap as hedging instrument. The advantage of using the perpetual became especially evident during 2021, but it is only for out-of-the-money put options that smile-implied deltas can significantly out-perform the standard Black-Scholes delta.