Polymarket Greeks — Delta, Theta, Vega for binary outcomes

Why binary outcomes have Greeks

A Polymarket YES/NO market is a digital (binary) option. The price between 0 and 1 is the market’s implied probability of resolution, which equals the option’s delta — the dollar-PnL sensitivity to a unit move in fair value. Time to resolution behaves like option expiry: as you approach it, price collapses toward 0 or 1 and uncertainty drains out of the position. That convergence is theta. And the standard deviation of price moves between now and resolution acts like implied vol — the bigger the spread and the choppier the price, the higher the realized volatility we surface as a vega-analog.

Treating positions this way isn’t just terminology. It gives a portfolio manager the same primitives they use on options: aggregate delta exposure, daily theta burn, concentration by event, and what-if PnL across hypothetical price moves.

Delta

For a single position holding shares of a binary YES token at price p, delta is just p. Multiplying by position size gives you the position’s dollar delta: the move in PnL you should expect for a 1.0 move in fair value. Holding 100 shares of a YES priced at 0.42 means you have $42 of dollar-delta exposure to that question.

delta = current_price
dollar_delta = size × delta

Theta

Theta captures how fast a position decays toward its terminal value (0 or 1) as resolution approaches. The pinch factor p × (1 − p) maxes at 0.25 when p = 0.5 — that’s when the outcome is most uncertain and theta hits hardest. It collapses as p approaches 0 or 1 (the market is already certain, so further passage of time doesn’t move the price much).

The Workstation surfaces theta as a $/day number. Negative if you’re short the volatility (selling premium near resolution); positive if you’re paying it.

theta_per_day = size × p × (1 − p) / hours_to_resolution × 24

Vega-analog

Real Black-Scholes vega doesn’t apply to a binary outcome (no continuous distribution to derive it from), but a useful proxy for the workstation is realized-vol-times-notional. We compute the trailing 7-day realized volatility of the mid-price from the same 1-minute bars that drive the IV-rank screener, then multiply by position notional. That gives a $/1σ-vol-move estimate per position — useful for sizing into news cycles.

Portfolio aggregates

The Risk dashboard rolls per-position Greeks into three numbers you watch on a single screen:

• Total notional — sum of size × current_price across all open positions.
• Σ delta (USDC) — same as total notional in the binary case (delta is just price); useful when you mix in other position types later.
• Σ theta / day — the daily decay your book is paying or earning. Negative is fine if it matches your strategy (e.g., gamma scalping). Big and negative without a thesis is a flag.

Concentration heatmaps

Polymarket events often have multiple markets that resolve from the same underlying outcome. The Workstation joins each position’s event_id and category metadata (populated from the Gamma API) so you can see concentration both ways: by event ("you have $5,000 of exposure to the Trump-2024 election event across 4 markets") and by category ("75% of your book is political").

What-if scenarios

POST /workstation/positions/whatif takes a list of (token_id, hypothetical_price) pairs and returns the PnL delta versus your current book. It runs in milliseconds against the same in-memory portfolio snapshot the Greeks endpoint reads from, so you can answer "what does my book look like if Trump wins" without touching the live order surface.

The matching event-pin stress test — pin an event to YES or NO and roll out the resolution PnL across every position attached to it — is on the roadmap and not yet a server endpoint. Today you reproduce it by sending each token in the event to /whatif at price 1.0 (or 0.0); the dedicated route lands when the catalyst-calendar event groupings ship.

Time-decay calendar

Every position has a resolution date enriched from Gamma. The Workstation sorts your book by next-to-resolve and colours each row by exposure size, so you always know what’s about to settle and what’s sitting on the back burner. This is the Polymarket equivalent of an options trader’s earnings calendar.