Empirical forward price distribution from Bitcoin option prices

Abstract

Report presents analysis of empirical distribution of future returns of bitcoin (BTC) from BTUSD inverse option prices. Logistic pdf is chosen as underlying distribution to fit option prices. The result is satisfactory and suggests that these prices can be described with just three or even one parameter. Fitted Logistic pdf matches forward price movements upto a scaling factor. Nevertheless, this observation stands alone and does not allow stochastic description of underlying prices with logistic pdf in similar fashion as it is done within Black-Scholes modelling framework. Put-call parity relationship is derived connecting prices of vanilla inverse options and futures.