Hedging Cryptocurrency Options

The cryptocurrency (CC) market is volatile, non-stationary and non-continuous. This poses unique challenges for pricing and hedging CC options. We study the hedge behaviour and effectiveness for a wide range of models. First, we calibrate market data to SVI-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate price paths using two types of Monte Carlo simulations. In the first approach, price paths follow an SVCJ model (stochastic volatility with correlated jumps). The second approach simulates paths from a GARCH-filtered kernel density estimation. In these two markets, options are hedged with models from the class of affine jump diffusions and infinite activity L\'evy processes. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. Dynamic Delta, Delta-Gamma, Delta-Vega and minimum variance hedge strategies are applied. The calibration results reveal a strong indication for stochastic volatility, low jump intensity and evidence of infinite activity. With the exception of short-dated options, a consistently good performance is achieved with Delta-Vega hedging in stochastic volatility models. Judging on the calibration and hedging results, the study provides evidence that stochastic volatility is the driving force in CC markets.