# Empirical forward price distribution from Bitcoin option prices

## TL;DR

This paper analyzes the empirical distribution of Bitcoin's future returns using option prices, fitting a logistic distribution that simplifies the description of forward prices but does not enable stochastic modeling like Black-Scholes.

## Contribution

It introduces a logistic distribution model for Bitcoin option prices and derives a put-call parity for inverse options and futures.

## Key findings

- Logistic pdf fits Bitcoin option prices well
- Forward price movements can be scaled with a logistic distribution
- The logistic model does not support stochastic price modeling like Black-Scholes

## 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.