Modeling Bitcoin Volatility: A Dual Perspective Analysis

Speaker: Prof. Abootaleb Shirvani, Dept. of Mathematical Sciences, Kean University

Abstract: Understanding the volatility of speculative assets is critical for investment decisions. Given that Bitcoin is considered, at least by some, a potential alternative to fiat money, its volatility characteristics are of particular concern. It is, therefore, essential to comprehend and appropriately model the process governing Bitcoin’s volatility.

In this presentation, we offer two perspectives for analyzing Bitcoin’s volatility. First, we introduce a doubly subordinated Levy process called the Normal Double Inverse Gaussian to model the time series properties of the cryptocurrency Bitcoin. We also developed an arbitrage-free option pricing model based on the NDIG process, providing a fresh perspective on Bitcoin valuation.

Within this model, we derive two distinct measures of Bitcoin volatility. The first measure combines NDIG option pricing with the Chicago Board Options Exchange VIX model to compute an implied volatility measure that reflects the viewpoints of options traders. The second measure investigates implied volatility in the real world, considering the perspectives of spot traders and utilizing an intrinsic time formulation.

Both volatility measures are compared to a historical standard deviation-based volatility. With appropriate linear scaling, the NDIG process perfectly captures the observed in-sample volatility.