Deriving Risk-Neutral Bitcoin Distributions from SVI Option Prices
Summary
The document explains how a calibrated SVI volatility surface can be used to estimate option prices across a range of strikes, then apply the Breeden-Litzenberger relationship. That relationship connects the second strike derivative of call prices to a risk-neutral probability density. The resulting probability density function and cumulative distribution function provide a way to interpret option prices as an implied distribution for an underlying asset, illustrated with Bitcoin options.
The example describes the probability assigned to Bitcoin finishing above a stated price at a specified expiry, and notes that the distribution can change over time. It observes that a rising underlying price can shift the distribution toward higher prices, while rising implied volatility can flatten its peak. These are market-implied, risk-neutral probabilities, not guaranteed forecasts or objective probabilities. Traders can compare them with their own assumptions to identify possible trade ideas, but the article offers no assessment of predictive accuracy or transaction costs.
Key ideas
- A calibrated SVI surface can generate option prices across a range of strikes.
- The Breeden-Litzenberger relationship maps the curvature of call prices across strikes to a risk-neutral density.
- The cumulative distribution expresses the market-implied probability of finishing above or below a price threshold.
- Changes in the underlying and implied volatility can shift or flatten the implied distribution.
- Market-implied probabilities can be compared with a trader’s own views, but they are not guaranteed forecasts.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.