Pricing virtual currency-linked derivatives with time-inhomogeneity

Abstract

In this study, we provide a theoretical exploration of cryptocurrency option pricing under the presence of regime-switching cryptocurrency prices with jumps and state-dependent interest rates. The properties of cryptocurrency returns are empirically investigated, and the European-style cryptocurrency options are priced when the dynamics of the cryptocurrency price and the instantaneous forward interest rate are, respectively, driven by a two-factor, state-dependent stochastic volatility model with jumps and a state-dependent Heath-Jarrow-Morton model. Under an incomplete market setting, we employ a dynamic measure change technique to determine a pricing kernel and state-dependent risk premiums and then derive the option pricing formula. Numerical illustrations verify the superior pricing performance of proposed model over competing models, and empirical results show the fitness of the proposed model.