Options 101 for Polymarket — and why every prediction market is already an option

§1 · Vanilla options

What is an option?

An option is a contract that gives its buyer the right — but never the obligation — to transact an underlying asset at a fixed price by a fixed time. The seller of the contract takes on the obligation, and is paid a premium up front for accepting that asymmetry.

• Call option — right to buy the underlying at the strike price K, before the expiry T.
• Put option — right to sell the underlying at K before T.
• Premium — what the buyer pays. This is the option’s market price.
• Payoff at expiry — what the contract is worth at T: max(S − K, 0) for a call, max(K − S, 0) for a put, where S is the underlying’s settlement price.

Vanilla options have continuous payoffs above (or below) the strike. A different breed — binary (digital) options — pay a fixed amount the moment the price crosses the strike. We’ll come back to those, because they’re what Polymarket sells.

§2 · Implied volatility

What is IV?

An option pricing model (Black-Scholes is the canonical one) takes five inputs: spot price, strike, time to expiry, risk-free rate, and volatility. The first four are observable. Volatility — how much the underlying is expected to move per unit time — is the market’s opinion. So we run the model backwards: given the option’s market price, what volatility must the market be assuming?

The number that falls out is implied volatility (IV), expressed as an annualized standard deviation. An IV of 30% on an equity option means the market expects the underlying to move ±30% per year (one standard deviation).

Two practical things to know:

• IV ≠ realized vol. IV is forward-looking (priced in); realized vol is what actually happened. Their gap (the "variance risk premium") is the edge most option-selling strategies capture.
• Different strikes trade with different IVs. Plot IV against strike and you get a U-shape (a smile) or a tilted U (a smirk). Add the time-to-expiry axis and you get the IV surface.

§3 · The IV surface

What is an IV surface?

The IV surface is a 3-D plot: strike on x, time-to-expiry on y, and implied vol on z. Two slices that traders look at constantly:

• Smile / skew — IV vs strike at a fixed expiry. Tells you how the market prices tail risk.
• Term structure — IV vs expiry at a fixed strike. Tells you whether near-dated or far-dated vol is rich.

Pockets where the surface dips or spikes are where vol traders look for relative-value plays — sell the rich part, buy the cheap part, hedge the residual delta.

§4 · Binary (digital) options

Binary options vs vanilla

A binary call pays a fixed amount (say $1) if the underlying finishes above the strike at expiry, and $0 otherwise. A binary put is the mirror image. The payoff is a step function — the value either jumps to the fixed amount or stays at zero, with no upside above the cliff.

Three properties fall out of the binary payoff:

• Price ≈ probability. Under a no-arb pricing model, the price of a $1-paying binary call equals the risk-neutral probability that the underlying finishes above the strike. The market literally tells you what it thinks the odds are.
• Delta = price. Sensitivity to a unit move in fair value equals the price itself, in the limit. Hold 100 shares of a YES priced at 0.42 and you have $42 of dollar-delta exposure to that question.
• Theta peaks at p = 0.5. The pinch factor p × (1 − p) in the theta formula maxes at 0.25, so time decay is heaviest when the outcome is most uncertain and collapses as the market becomes confident.

§5 · The mapping

Why every Polymarket market is already an option

Polymarket pays out exactly $1.00 per share to the winning side and $0.00 to the losing side. That is a binary call on the YES outcome (and equivalently a binary put on the NO outcome). The price you pay between 0 and 1 is the option premium — and by the price-equals-probability property above, it’s also the market’s implied probability that YES wins.

That’s the workstation thesis. Binary outcomes are options. The only missing piece is the tooling to trade them like options — which is the order types, Greeks, screeners, and multi-leg tickets PolyZig ships.

§6 · IV-rank — the Polymarket version

Why we use realized-vol percentile, not implied vol

On a vanilla option chain you can back out IV from each strike’s quoted price. On Polymarket you can’t — there’s only one strike (the question outcome) and the price IS the probability, with no separate vol input to back out.

So the Workstation uses realized vol instead. We persist 1-minute OHLC bars per market (see the methodology page), compute trailing realized vol over a 252-trading-day-equivalent window, and rank the current value within that window. A market at the 95th percentile is bouncing more than it has all year — historically a good signal that directional plays and OCO brackets work well. A market at the 5th percentile is pinned — historically a signal to sell premium against the residual gap to $0 or $1.

Same playbook as IV-rank in equity options. Same use case: regime identification.

§7 · The Polymarket vol surface

The realized-vol surface analog

The IV-surface analog on Polymarket is a 2-D heatmap of realized vol indexed by market × days-to-resolution. Markets far from resolution behave like long-dated options (more uncertainty, slower theta); markets near resolution behave like short-dated options (sharp price moves, accelerating theta).

Spot a market that’s historically quiet but its days-to-resolution bucket runs noisy — that’s a regime mismatch worth investigating. The Workstation’s screeners + risk dashboard surface the data; the interpretation is yours.

§8 · From here

Reading order through the rest of the workstation

1. Δ and Θ for binary outcomes — closed-form math + worked example with the pinch-factor table.
2. Order types for prediction markets — every order primitive an options desk uses, layered on Polymarket’s CLOB.
3. Screeners — IV-rank, theta-harvest, mispricing, and the catalyst calendar.
4. Multi-leg structures — verticals, calendars, pairs, and box-spread arbitrage with payoff diagrams.
5. Glossary — every term defined, with formulas and links back to the methodology pages.

References

Where to go deeper

• Hull, J. C. Options, Futures, and Other Derivatives. 11th ed., Pearson, 2021. The textbook. Read chapters 9–15 for vanilla, 19 for Greeks, 26 for digitals.
• Sinclair, E. Volatility Trading. 2nd ed., Wiley, 2013. The practitioner volume on IV-rank, term structure, and realized-vs-implied.
• Wystup, U. FX Options and Structured Products. 2nd ed., Wiley, 2017. Chapter on digital options has the cleanest derivation of binary Greeks.
• Wolfers, J. & Zitzewitz, E. Prediction Markets. Journal of Economic Perspectives 18(2), 2004. The case for treating prediction market prices as implied probabilities.
• Manaster, S. & Mann, S. C. Life in the Pits: Competitive Market Making and Inventory Control. Origin of the spread-tightness signal used in the screener.

FAQ

Common questions