[Paper Review] Pricing Cryptocurrency Options

Ai Jun Hou, Ning Wang+2 more|Explore Bristol Research|Sep 23, 2020

Stochastic processes and financial applications33 references55 citations

TL;DR

The paper evaluates affine stochastic volatility with jumps (SVCJ), SVJ, and Burstein–Ricci (BR) style models for Bitcoin and a cryptocurrency index to price European options, using Bayesian estimation and Monte Carlo simulations, with revisions focusing on SV-based models and robustness.

ABSTRACT

Cryptocurrencies, especially Bitcoin (BTC), which comprise a new digital asset class, have drawn extraordinary worldwide attention. The characteristics of the cryptocurrency/BTC include a high level of speculation, extreme volatility and price discontinuity. We propose a pricing mechanism based on a stochastic volatility with a correlated jump (SVCJ) model and compare it to a flexible co-jump model by Bandi and Renò (2016). The estimation results of both models confirm the impact of jumps and co-jumps on options obtained via simulation and an analysis of the implied volatility curve. We show that a sizeable proportion of price jumps are significantly and contemporaneously anti-correlated with jumps in volatility. Our study comprises pioneering research on pricing BTC options. We show how the proposed pricing mechanism underlines the importance of jumps in cryptocurrency markets.

Motivation & Objective

• Motivate pricing of cryptocurrency options amid jumps and stochastic volatility.
• Compare affine jump-diffusion models (SVCJ, SVJ, BR) for BTC and CRIX dynamics.
• Assess model fit and implications for option pricing via simulation-based methods.
• Provide data sources, robustness checks, and guidance for institutional interpretation of results.

Proposed method

• Estimate BTC and CRIX dynamics under SVCJ, SVJ, and BR models within a Bayesian framework.
• Calibrate models to price paths and compute European option values via Monte Carlo simulations.
• Compare models using goodness-of-fit metrics and diagnostic plots (e.g., MSE, QQ plots).
• Assess the sensitivity of option prices to model choice and parameter values.
• Document data sources and provide code availability references (Quantlets).

Figure 1: Call option price differences between the SVCJ and SVJ models, and between the BR and the SVJ models: BTC

Experimental results

Research questions

• RQ1 Do affine jump-diffusion models (SVCJ, SVJ, BR) capture Bitcoin and CRIX price dynamics better than alternatives?
• RQ2 How do the different models influence the pricing of European cryptocurrency options?
• RQ3 What is the robustness of results to data sources and estimation choices, such as initial values and priors?
• RQ4 Can the empirical implied volatility surfaces under these models exhibit market-like skews for Bitcoin and CRIX?

Key findings

• The SVCJ model often yields a better fit (lower MSE) than SVJ in the reported diagnostics.
• Option prices generated under the SVCJ and BR models show specific behaviors across moneyness and maturity, informing curvature of the implied volatility surface.
• The authors provide a detailed replication-friendly data and code ecosystem (Quantlets) and emphasize Bayesian estimation with parameter uncertainty considerations.
• Robustness steps include moving ARIMA and GARCH components to Appendix and focusing on SV-based dynamics relevant for option pricing.
• Across revisions, the correlation between Bitcoin dynamics and broader crypto indices is discussed and contextualized for institutional use (e.g., CRIX vs BTC).