The least efficient approach: max loss per trade
If a market maker is shortq_c calls and q_p puts at the same strike K, the simple approach adds each trade’s maximum possible payout:
S_T = 1) and the put’s worst case (S_T = 0) as if they could both occur. But the YES price cannot finish at 0.00 simultaneously. For a mixed book, that over-collateralizes: it locks the cost of two mutually exclusive disasters.
For a multi-strike or multi-market book, the same effect repeats. Worst cases are stacked across strikes and markets that cannot all resolve against the maker at once. The simple approach leaves a lot of maker capital sitting idle.
Smart Margin: net the payoffs
Smart Margin starts from the same payoff definitions:K:
S_T is a single number.
For a short book of q_c calls and q_p puts at strike K, the total payout owed is q_c C_K(S_T) + q_p P_K(S_T). Because S_T is bounded on [0, 1], the worst case is reached at one of the two endpoints:
So Smart Margin locks the larger of the two mutually exclusive outcomes:
Which endpoint dominates?
Letdelta = q_c − q_p, so q_c = q_p + delta. The condition for which boundary has the larger payout is:
- If
q_p(2K − 1) > delta(1 − K), the worst case isS_T = 0and the collateral isq_p × K. - If
q_p(2K − 1) < delta(1 − K), the worst case isS_T = 1and the collateral isq_c × (1 − K). - If the two expressions are equal, both endpoints require the same collateral.
Numerical examples
100 short calls and 100 short puts at K = $0.70
100 short calls and 100 short puts at K = $0.70
q_c = 100,q_p = 100,K = 0.70,delta = 0- Simple max loss:
100 × 0.30 + 100 × 0.70 = $100 - Smart Margin:
max(100 × 0.70, 100 × 0.30) = $70 - Capital saved: 30% for this strike
50 short calls and 150 short puts at K = $0.60
50 short calls and 150 short puts at K = $0.60
q_c = 50,q_p = 150,K = 0.60,delta = -100- At
S_T = 0:150 × 0.60 = $90 - At
S_T = 1:50 × 0.40 = $20 - Smart Margin:
max(90, 20) = $90 - Simple max loss would be
50 × 0.40 + 150 × 0.60 = $110
One-sided book: 100 short calls at K = $0.50
One-sided book: 100 short calls at K = $0.50
q_c = 100,q_p = 0,K = 0.50- Smart Margin:
max(0 × 0.50, 100 × 0.50) = $50 - This is the same as the simple per-trade max loss, because there is nothing to net.
Extending across strikes and markets
A real market-making book contains many strikes and many prediction markets. For each underlying the final price is still bounded on [0, 1], so the total portfolio payoff is a piecewise-linear function of a finite set of prices. The true worst case of the whole book is found at boundary points and strike points. Smart Margin evaluates that function across all of a maker’s open shorts and returns a single portfolio-level collateral number. Because it nets offsetting exposures, it reduces the capital required for multi-strike and multi-market books the same way it does for a single strike: the collateral is the actual worst case of the combined surface, not the sum of isolated maxima.What this means for market makers
- More capital stays available for quoting. Less USDC is locked against payouts that cannot happen at the same time.
- Two-sided markets become economical. A maker can comfortably quote both calls and puts around the same strike without doubling the collateral.
- Multi-strike and multi-market books scale better. Portfolio-level netting replaces position-by-position stacking of worst cases.
- Collateral matches the real risk. It is sized to the true worst-case payout of the book, not a conservative sum of mutually exclusive extremes.
