I'm currently studying financial derivatives and I've become particularly interested in cryptocurrency options, specifically Bitcoin. Given the unique characteristics of Bitcoin and other cryptocurrencies (e.g., high volatility, 24/7 trading), I'm curious about the most accurate models or methods for pricing Bitcoin options or at least estimating risk-neutral PDF to imply probability of reaching a certain price.

Traditional models like Black-Scholes seem ill-suited due to assumptions that don't hold for Bitcoin. Are there alternative models that have proven more accurate in the context of Bitcoin? Are there modifications to traditional models that make them more applicable to cryptocurrencty options?

Any insights or references to relevant research would be greatly appreciated.

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    $\begingroup$ People use BS as a convenient way to quote volatility, not so much to price when BS assumptions are too simple, more complicated models to actually price and risk manage. Can you please clarify what features of crypto you refer to that "traditional" approaches fail to model? Volatile implied volatilities? Premium quoted in underlying crypto (inversed), rather than in fiat currency? Check out doi.org/10.3389/frai.2019.00005 (2019)for review of literature. $\endgroup$ Mar 17 at 19:19
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    $\begingroup$ Of anything, 24/7 trading gets you closer to the Black Scholes world. FX markets are also open 24h during the week. I think getting RN probabilities should work exactly the same way as for any other asset class. The usefulness of these probabilities is is a different question. IMHO, Probabilistic statements derived from options are only valid in the risk-neutral world and you simply cannot use these to make statements about the probabilities of events occurring in the real world. $\endgroup$
    – AKdemy
    Mar 17 at 19:38

1 Answer 1


Welcome to the forum. I don't have an answer for you, but in options pricing, it is important to choose the stochastic process that accurately describes the dynamics of the underlying asset.

For example, maybe choosing stochastic volatility models is better suited for Bitcoin rather than constant volatility models than Black-Scholes.

From there on, you could probably use Monte Carlo to simulate the potential price paths (which is a options pricing model an approach you can use to go about pricing your option after picking your model - stochastic/local vol).

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    $\begingroup$ Monte Carlo simulation is not a model generally speaking. It's a methods that can be applied on a model (e.g. Black Scholes) to find solutions. $\endgroup$
    – user70573
    Mar 17 at 19:05
  • $\begingroup$ Thanks, you are right, made some modifications for the purpose of clarity. $\endgroup$
    – KaiSqDist
    Mar 17 at 19:14

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