Estimating Bitcoin Risk-Neutral Probabilities from Noisy Options
Summary
The document discusses estimating Bitcoin’s risk-neutral price distribution from Deribit option prices, including probabilities that the price will fall within selected ranges. It identifies wide bid-ask spreads as a source of noisy inputs: using midpoint quotes directly may distort probabilities derived through methods such as Breeden-Litzenberger or numerical integration. The response recommends caution with the interpretation as well as the data quality, since option-implied probabilities are risk-neutral quantities and may differ substantially from real-world outcomes.
A smooth, arbitrage-free volatility surface can make the resulting distribution less erratic, while the surface’s shape and volatility skew affect the inferred probabilities. The response also points to a published approach for constructing option-based risk-neutral distributions. It does not specify a definitive bid-ask adjustment, quote filtering rule, or smoothing procedure, nor does it provide a worked Bitcoin estimate. The practical lesson is to build a coherent volatility surface and treat the probabilities as pricing-model outputs rather than forecasts of actual frequency.
Key ideas
- Option prices can be used to infer risk-neutral price distributions through derivatives of prices or numerical integration.
- Wide bid-ask spreads make midpoint-based estimates sensitive to noisy quotes.
- A smooth, arbitrage-free volatility surface can reduce choppiness in inferred probabilities.
- Risk-neutral probabilities need not match real-world probabilities.
- Volatility skew and surface shape influence the estimated distribution.
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Full text
# How to compute implied probability of Bitcoin price given noisy option data? # How to compute implied probability of Bitcoin price given noisy option data? I am trying to calculate the implied probabilities of Bitcoin being within specific price ranges using option chains from Deribit. The challenge I am facing is dealing with bid-ask spreads, which are typically in the range of 5-10%, even for the most liquid strike prices. Here’s what I have so far: I understand that the risk-neutral probabilities of certain price ranges can be derived from option prices using techniques like the Breeden-Litzenberger formula or through numerical integration of the price distribution implied by the market. However, due to the relatively wide bid-ask spreads (5-15%) , the mid-point price might not fully capture the true market consensus, potentially skewing the derived probabilities. Questions: What are the best practices for handling wide bid-ask spreads in this context? Should I use the mid-point price, or are there alternative approaches to ensure more accurate implied probabilities? Are there any adjustments or smoothing techniques recommended for noisy data from real-world option chains with such spreads? How would incorporating a volatility surface or implied volatility skew affect the computation of probabilities? ## Answer by AKdemy (score 7) https://quant.stackexchange.com/a/81777 Deribit data seems noisy in general, https://quant.stackexchange.com/a/81592/54838. That said, I would be extremely cautious using risk neutral implied probabilities. Any probabilistic statements derived from options are only valid in the risk-neutral world and may have very little to do with actual real world probabilities. A properly computed vol surface would be smooth and arb free. Therefore, computing the probability will be better (less choppy). You can find plenty of details in two excellent answers from @Quantuple: - https://quant.stackexchange.com/a/24922/54838 and - https://quant.stackexchange.com/a/29532/54838 for actual code. An alternative (similar approach) is shown by Malz in the Fed Staff Report No. 677 on June 2014 A Simple and Reliable Way to Compute Option-Based Risk-Neutral Distributions. I used it in an answer to Option Pricing for Illiquid case, which also shows the impact of different shapes of the vol surface on the implied probabilities.
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