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Fitting Bitcoin Inverse Option Prices with a Logistic Forward Distribution

Article arXiv papers · Author: Nikolai Zaitsev
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Summary

The report examines whether prices of BTUSD inverse options can be represented by an empirical distribution of future Bitcoin returns. It fits a logistic probability density to option prices and reports that the fit is satisfactory, with the distribution described using as few as three or even one parameter. The fitted shape corresponds to forward price movements after applying a scaling factor.

The document also derives a put-call parity relationship linking vanilla inverse option prices with futures prices. Its main limitation is that the observed fit is not evidence for a complete stochastic price model: the report cautions that this result alone does not justify modeling Bitcoin prices with logistic dynamics in the manner of Black-Scholes. No detailed sample description or numerical fit statistics are provided in the supplied text.

Key ideas

  • A logistic probability density is fitted to BTUSD inverse option prices to represent future Bitcoin returns.
  • The report describes the fit as satisfactory and says it can use a small number of parameters.
  • The fitted distribution tracks forward price movements after scaling.
  • A put-call parity relationship connects vanilla inverse options and futures.
  • The empirical fit alone does not establish a stochastic pricing model comparable to Black-Scholes.

Tags

CryptoOptionsFuturesDerivatives pricingStatistics
Full text
# Empirical forward price distribution from Bitcoin option prices


# Empirical forward price distribution from Bitcoin option prices









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.