Hedging strategies under jump-induced market incompleteness

Abstract

Simulierte Hedge Missspezifikation zu Risikomanagementzwecken von Cryptocurrencies.

The market for cryptocurrencies is a very dynamic market with highly volatile movements and discontinuities from large jumps. We investigate the risk-management perspective when selling securities written on cryptocurrencies. To this day, options written on cryptocurrencies are not officially exchange-traded. This study mimics the dynamics of cryptocurrency markets in a simulation study. We assume that the asset follows the stochastic volatility with correlated jumps model as presented in Duffie et al. ( 2000 ) and price options with parameters calibrated on the CRIX, a cryptocurrency index that serves as a representative of market movements. We investigate on risk- management opportunities of hedging options written on cryptocurrencies and evaluate the hedge performance under model misspecification. The hedge models are misspecified in the manner that they include fewer sources of randomness than the nother the ment the ment the industry-standard Black-Scholes option pricing model, the Heston Stochastic volatility model, and the Merton jump-diffusion model. We present different hedging strategies and perform an empirical study on delta-hedging. We report poor hedging results when calibration is poor. The results show good performances of the Black-Scholes and the Heston model and outline the poor hedging performance of the Merton model. Lastly, we observe large unhedgeable losses in the left tail. These losses potentially result from large jumps.