Bitcoin Volatility and Intrinsic Time Using Double Subordinated Levy Processes

TL;DR

This paper introduces a novel doubly subordinated Levy process called NDIG to model bitcoin's price dynamics, capturing its skewness and fat tails, and provides two methods for measuring bitcoin volatility that align well with observed data.

Contribution

The paper develops the NDIG process, a new stochastic model for bitcoin prices, and derives two innovative volatility measures that match observed market volatility.

Findings

NDIG accurately captures bitcoin's skewness and fat tails.

The proposed volatility measures align with observed in-sample volatility.

NDIG-based implied volatility correlates with market data.

Abstract

We propose a doubly subordinated Levy process, NDIG, to model the time series properties of the cryptocurrency bitcoin. NDIG captures the skew and fat-tailed properties of bitcoin prices and gives rise to an arbitrage free, option pricing model. In this framework we derive two bitcoin volatility measures. The first combines NDIG option pricing with the Cboe VIX model to compute an implied volatility; the second uses the volatility of the unit time increment of the NDIG model. Both are compared to a volatility based upon historical standard deviation. With appropriate linear scaling, the NDIG process perfectly captures observed, in-sample, volatility.