Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2021 021

Hedging Cryptocurrency Options

Jovanka Matic
Natalie Packham
Wolfgang Karl Härdle

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 Lévy 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.


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