Essay · Quant & Markets

Options vs the Crowd: Deribit and Polymarket

I built a tool to read a probability out of Bitcoin options and bet against Polymarket when the two disagreed. The disagreement was real. The trade was not. This is the honest version.

Polymarket runs binary prediction markets. "Will Bitcoin be above $70,000 on Friday?" pays a dollar if yes and nothing if no, so its price is a probability the crowd has voted on. Deribit's deep options market on the same Bitcoin has its own opinion. Two venues, one underlying: if they disagree about how likely $70,000 is, one is wrong and the gap is money. The tool that measures the gap works. As a trading idea it is a polite way to lose money.

Up front, so it is not buried: every result here is from a paper-traded book, not real capital. Paper trading exists to kill ideas that do not survive contact with the market, and this one did not.

Turning an Option Price Into a Probability

An option already contains a probability; the job is to extract it. The key choice is to price off the forward (what futures quote for settlement) rather than spot, an approach called Black-76. It matters: an early version that guessed a fixed drift instead of reading the forward had a zero per cent win rate on one whole side of its trades. With it, the probability Bitcoin finishes above a strike is one line of Black-Scholes:

P(S_T > K) = N(d₂), d₂ = ( ln(F/K) − ½σ²T ) / ( σ√T )

The only hard input is sigma, the implied volatility, and it is not one number: every strike trades at its own, tracing a curve called the smile. To price a strike with no clean quote you fit a smooth SVI curve through it, flexible enough to track the smile, constrained enough to stay arbitrage-free.

The Interactive: Watch the Two Curves Disagree

A snapshot from that machinery: a seven-day horizon, a forward of $68,000. The blue curve is the options-implied probability Bitcoin finishes above each strike; the amber curve is the crowd. Drag the marker to read off both, plus the gap.

Drag to move the strike. The blue line is the options model; the amber line is the crowd. Where they split is where the tool fired its trades.

Near the money the curves agree. Out at $80,000 they part company: the options model gives Bitcoin about a one per cent chance of getting there, the crowd says closer to eleven. A free ten-point edge.

Why the Edge Was a Mirage

The trade lost, not because the code was buggy, but because the disagreement is real and the crowd was right. Two reasons, both about what kind of probability each number is.

First, the measure problem. An options-implied probability is a risk-neutral, Q-measure number: not the honest chance of an event, but the chance after it is bent by what people pay to hedge against it. Investors overpay for crash protection, so option prices overstate big moves; on Bitcoin that premium runs to ten or fourteen points of variance. Polymarket sits closer to a physical probability. Net them and most of what you call "edge" is that premium: fair value, booked as profit.

Second, information asymmetry. The crowd reads the news and knows when a court ruling or an ETF decision is coming; a volatility surface fitted to options quotes does not. When the crowd prices a tail at eleven per cent and the surface says one, the crowd is often pricing a catalyst the surface cannot see. The model was not finding mispricing, it was advertising its own blind spots.

The core finding: across the paper book, the options model's probabilities scored a Brier of about 0.30 against actual outcomes; the Polymarket mid-prices on the same events scored about 0.13. The crowd was roughly twice as good at predicting what happened. The tool was not measuring how wrong Polymarket was. It was measuring how wrong the tool was.

What I Tried Before Admitting It

When a model disagrees with reality the instinct is to assume it needs a better fit, so I spent real effort there: a haircut shrinking implied volatility toward realised, a smile weighted by each option's vega. Both moved the Brier score by a few thousandths against a gap of about 0.16: statistically real, economically meaningless. No fit turns one kind of probability into the other.

The one cut that mattered was tenor. On one-to-three-day horizons the trade was marginally alive; on three-to-seven days it was a bloodbath, because slow markets give others time to arbitrage out any genuine mispricing, leaving only the structural gap. Short tenors made a bad book less bad. Never a good one.

The Useful Inversion

The failure produced one valuable thing: a sign flip. If the options market overprices tails because of the risk premium, the trade is not to bet against the crowd but to sell that premium on the options venue, collecting the structural gap instead of paying it. The bug was the feature, read backwards.

So I am keeping the tool, as a measuring instrument rather than a money printer. The interesting reading was never "the crowd is wrong," it was "here is what the crowd's calibration is worth, and it is more than you think."

For the longer version of why a better fit never closed the gap, see the volatility-surface postmortem. A sibling failure, the high-frequency directional strategy, died for a different reason.