A Kalshi or Polymarket contract that pays $1 if BTC settles above a strike is a cash-or-nothing digital call, so the natural hedge is a tight call spread on Deribit sized to the contract’s payout. Its fair value is the risk-neutral probability of finishing above the strike, and that probability should be read from the Deribit volatility surface, including skew, rather than from at-the-money vol. What’s left after the hedge is basis: different settlement indices, different settlement times, the strike grid and fees.

Below: pricing, replication, a worked example and running both legs in one book. For wider context, see Kemet for prediction markets.

The event contract is a digital option

A contract such as “BTC above $104,000 at 5pm ET Friday” pays $1 per contract if the condition is met and $0 otherwise. In options terms it is a cash-or-nothing digital call with strike K and expiry T. With forward F, volatility σ and rate r, the Black-Scholes value is:

D = e^(-rT) × N(d2), where d2 = [ln(F/K) - σ²T/2] / (σ√T)

N(d2) is the risk-neutral probability of finishing above K. A Yes price of $0.30 says that probability is roughly 30%.

Why at-the-money vol gives the wrong probability

Crypto options carry a smile, so σ depends on strike. A digital is the limit of a call spread, which means its price is the negative slope of the call price curve in strike:

D = -dC/dK = e^(-rT) × N(d2) - Vega × dσ/dK

The first term is the flat-vol answer at the strike’s own implied vol. The second is the skew adjustment: where vol falls as strike rises (dσ/dK < 0) it adds value, and where vol rises with strike it subtracts. Using at-the-money vol ignores both. For a given skew slope the error is largest near the money and grows with tenor, and because crypto skew is often steepest at short tenors, check it on every contract rather than assume it is small. Price the digital as a call spread off the live Deribit surface.

Replicating the digital with a Deribit call spread

Buy a call at K – h/2 and sell a call at K + h/2. One spread of width h, on 1 BTC, pays between $0 and $h at expiry. To replicate a digital paying P dollars, you need P/h spreads. Deribit BTC options are 1 BTC per contract, available as inverse options settled in BTC or as linear options settled in USDC, so the count of spreads is also the BTC quantity on each leg.

The centered spread estimates fair value. To cover a short digital in every state, end the spread at the strike: long K – h, short K. It pays the full P at or above K, super-replicating the short digital at a higher cost.

Worked example (illustrative numbers)

Every figure is hypothetical. Assumptions: BTC forward F = $100,000, seven days to expiry (T = 7/365), r = 0, at-the-money vol 50%, and implied vol falling 0.25 vol points per $1,000 of strike (49.50% at $102,000, 49.25% at $103,000, 49.00% at $104,000, 48.75% at $105,000). Both venues settle on the same price at the same moment.

• Black-Scholes call prices, USD per 1 BTC: $102,000 call $1,876; $103,000 call $1,516; $104,000 call $1,209; $105,000 call $951.
• Centered spread, long $103,000 / short $105,000 (h = $2,000): $1,516 – $951 = $565. Implied digital = 565 / 2,000 = 0.2825.
• Check with the formula at K = $104,000: N(d2) at 49% vol = 0.2703. Vega = $4,765 per 1.00 of vol. dσ/dK = -0.0025 per $1,000 = -0.0000025 per dollar. Skew term = -4,765 × -0.0000025 = +0.0119. D = 0.2703 + 0.0119 = 0.2822, matching the spread to within discretisation.
• At-the-money vol gives N(d2) = 0.2739, about 0.8 cents low. In this example the shortcut understates the probability; with a different skew it can overstate it.
• Super-replicating spread, long $102,000 / short $104,000: $1,876 – $1,209 = $667, or 0.3335 per $1 of payout.

Now suppose Kalshi Yes on “above $104,000” is bid at $0.36 and the desk sells $50,000 of payout, i.e. 50,000 contracts, collecting $18,000 (on Kalshi this is a purchase of 50,000 No at $0.64, so $32,000 is posted at the venue). The hedge is P/h = 50,000 / 2,000 = 25 spreads, 25 BTC per leg, which is also Deribit’s minimum block size for BTC options.

• Centered hedge: 25 × $565 = $14,125. The $3,875 difference is expected edge, not locked. Between $103,000 and $105,000 the spread’s ramp and the digital’s step diverge: just above $104,000 the desk owes $50,000 and the spread pays about $25,000.
• Super-replicating hedge: 25 × $667 = $16,675. Below $102,000 both pay zero. Between $102,000 and $104,000 the digital pays zero and the spread pays 25 × (S – 102,000), which is positive. At or above $104,000 the spread pays its $50,000 maximum against the $50,000 owed. The $1,325 difference is the minimum outcome before fees and settlement basis.

The event venue is pricing the digital 7.75 cents over the surface’s fair value (0.36 against 0.2825) and 2.65 cents over a hedge that covers every state. Those two numbers frame how much basis and execution cost the trade can absorb.

Where the hedge leaks

• Settlement index. Kalshi’s crypto price markets settle on a CF Benchmarks index named in the rules, for most markets the simple average of the CF Bitcoin Real-Time Index over the 60 seconds before the stated time. Polymarket’s daily “Bitcoin above” markets on its international venue, which is not available to US persons, have resolved on the close of the Binance BTC/USDT 1-minute candle at 12:00 ET. Deribit options settle on a time-weighted average of the Deribit index between 07:30 and 08:00 UTC. Three prices, three methods.
• Settlement time. Deribit expiries are at 08:00 UTC. An event resolving at noon or 5pm ET leaves a gap: take the next Deribit expiry and carry residual optionality, or hold open exposure between the prints.
• Pin risk. Near the strike the digital flips on a few dollars of index difference, so the basis between BRTI, Binance and the Deribit index bites hardest there.
• Strike grid. If the event strike sits between listed Deribit strikes, the spread is off-center and the replication approximate.
• Fees and collateral. Each venue charges fees, and margin sits in separate accounts: USD at Kalshi, pUSD on Polymarket’s international venue or USD on Polymarket US, BTC or USDC at Deribit.

Delta hedging instead of a spread

A desk can also hedge the digital dynamically with perps or futures. The digital’s delta per $1 of payout is:

Δ = e^(-rT) × n(d2) / (F × σ × √T)

In the example, $50,000 of payout carries about 2.4 BTC of delta (50,000 × 0.0000488). Near expiry with spot near the strike, √T shrinks and delta spikes, and gamma changes sign as spot crosses the strike. Rebalancing perps through that zone is expensive. The call spread holds its shape to expiry, so it is the core hedge and perps handle residuals.

Range and bucket contracts

A contract paying $1 if BTC settles between K1 and K2 equals a digital at K1 minus a digital at K2. That replicates as a long call spread at the lower edge and a short call spread at the upper edge: a condor, which approaches a butterfly as the bucket narrows. A ladder of buckets reads off the Deribit surface as a strip of butterflies.

Running both legs in one book with Kemet

Kemet connects to Kalshi, Polymarket and Deribit, along with Derive, OKX, Binance, Bullish, Hyperliquid and Coinbase, using the desk’s own venue accounts and API keys. Kemet is a technology provider: it does not hold client assets, take the other side or act as a broker. The workflow for this trade:

• Event contracts and options positions sit in one portfolio, with positions, Greeks and PnL normalised across venues. See cross-venue portfolio risk.
• Desks can see digital exposure from event contracts expressed as delta, gamma and vega next to their options book. Kemet runs this conversion automatically.
• The multi-leg package builder legs the call spread or condor as one order, sized from the payout and width.
• For size, the spread goes out as an RFQ on Deribit, Paradigm or Derive. More on that in crypto options RFQ and block trading.
• Auto-hedging with thresholds manages the residual delta from settlement-time and strike-grid mismatch.
• Execution algorithms work the event-contract side, which matters given the depth on Kalshi and Polymarket order books. For large prints, see block trading on Kalshi and Polymarket.

For venue-level detail, read the Kalshi API for institutional desks and Kalshi vs Polymarket for institutional desks. Kemet’s Kalshi integration was announced with FalconX: Kemet and FalconX bring institutional execution to prediction markets on Kalshi.

FAQ

How many Deribit spreads hedge my event contract position?

Divide the dollar payout by the spread width. $50,000 of payout hedged with a $2,000-wide spread needs 25 spreads, 25 BTC on each leg. A narrower width tracks the digital more closely and needs more contracts.

Can I hedge with perpetual futures instead?

For small positions or far from expiry, yes. Near expiry at the strike, a perp hedge needs heavy rebalancing; a call spread does not.

Do Deribit options settle at the same time as Kalshi or Polymarket contracts?

Generally not. Deribit settles at 08:00 UTC on a 30-minute index TWAP; Kalshi and Polymarket name their source and time in each market’s rules. Treat the gap as basis risk and size for it.

Does Kemet custody funds or take the other side?

No. Desks trade through their own venue accounts and keys, and Kemet rejects API keys with withdrawal rights.

If your desk trades event contracts against options, Book a demo to see the workflow on your own venue accounts.