Paper: arXiv 2506.14614

Authors: Julia Kończal

Abstract

The cryptocurrency options market is notable for its high volatility and lower liquidity compared to traditional markets. These characteristics introduce significant challenges to traditional option pricing methodologies. Addressing these complexities requires advanced models that can effectively capture the dynamics of the market. We explore which option pricing models are most effective in valuing cryptocurrency options. Specifically, we calibrate and evaluate the performance of the Black-Scholes, Merton Jump Diffusion, Variance Gamma, Kou, Heston, and Bates models. Our analysis focuses on pricing vanilla options on futures contracts for Bitcoin (BTC) and Ether (ETH). We find that the Black-Scholes model exhibits the highest pricing errors. In contrast, the Kou and Bates models achieve the lowest errors, with the Kou model performing the best for the BTC options and the Bates model for ETH options. The results highlight the importance of incorporating jumps and stochastic volatility into pricing models to better reflect the behavior of these assets.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a structured empirical comparison of benchmark option pricing models (Black-Scholes, Merton, Heston, Kou, Variance Gamma, Bates) applied to regulated BTC and ETH futures options across multiple maturities. While the theoretical framework relies on well-established closed-form and Fourier-transform pricing techniques rather than novel mathematical derivations, the empirical execution using market data from a turbulent period offers valuable insights for crypto derivatives.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Identify best option pricing models for BTC & ETH futures"] --> B["Models Calibrated:<br>Black-Scholes, Merton, VG, Kou, Heston, Bates"]
    B --> C["Input Data:<br>BTC and ETH Futures Vanilla Options"]
    C --> D["Process:<br>Calibrate models & calculate pricing errors"]
    D --> E["Findings:<br>Black-Scholes has highest errors"]
    D --> F["Optimal Outcomes:<br>Kou model best for BTC<br>Bates model best for ETH"]
    E & F --> G["Conclusion:<br>Must incorporate jumps & stochastic volatility"]

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1 of 40 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.