Conditional and Basket Event-Linked Perpetual Futures | Research

Working paper · SSRN 7646159 · Posted 21 Oct 2026

What do the funding rate and margin of a prediction-market perpetual become when the index is a conditional or a basket?

Anirban Majumdar · InnovationStrat Consulting, LLC · ORCID

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Key results

On the presidential pair the funding correction averaged 0.076 per year against a base term of 0.116, and exceeded it in absolute value on 50 percent of the days.
The conditional index's half-spread grows as 1/P(B); the listing floor for a five-cent tolerance is 0.148 at half a tick per leg and 0.296 at the effective spread.
The one-day 99 percent loss on a unit conditional position rises from 0.083 at P(B) = 0.5 to 0.48 at P(B) = 0.01.
At a matched 99 percent one-day shock the base grid charges 1.48 times the stress margin on a long basket and 1.80 times on a spread; at fixed ten-point shocks the ratios are 3.7 and 4.6.
Biden's nomination leg fell from 0.29 to zero in one day, after the joint market had traded above it on 29 of 189 days by up to 14 cents.

Summary

A derivative on a ratio of two markets

Prediction markets such as Kalshi and Polymarket list one kind of contract. It pays one if an event happens and nothing otherwise. In an earlier paper we built a perpetual future on a single such market, held to the market's probability index by a funding stream, and priced European options on the index off a logit-normal terminal law. A grid of probability and volatility shocks margined a book of both. Few of the risks a trader would want to hedge involve one market. Nechepurenko (2026b) classified the contracts that can be written on more than one market and proved a qualitative result for each, but priced none of them. This paper does the pricing for the conditional and the basket. The other five designs fold into those two or into the base case.

The conditional contract

The conditional index is the probability of A given B. On a venue it is the ratio of the joint market's price to the conditioning market's price. Under the measure conditioned on B it is a martingale. Under the pricing measure it drifts, and in a bivariate logit model the drift is a correlation term, -ρσcσb c(1-c)(1-b). The funding rate of a perpetual on the ratio is therefore the single-market identity plus a correction of that size with the opposite sign.

We calibrated two nested Polymarket pairs from 2024. The presidential pair sets the market on a Republican winning both the popular vote and the presidency against the market on Trump winning the presidency. There the correction averaged 0.076 per year against a base term whose mean absolute value was 0.116. Figure 1 plots both parts. The correction was positive every day and exceeded the base term in absolute value on 50 percent of the days. The sweep pair sets Trump winning every swing state against a Republican winning Pennsylvania. There the correlation was -0.13, and the correction averaged -0.117 against a base term of 0.563, about a sixth of it. The signs were opposite on the two pairs.

Figure 1. Upper panel: the Polymarket probability that Trump wins the 2024 presidency (the conditioning leg b), the probability that a Republican wins both the popular vote and the presidency (the joint leg q), and their ratio, the conditional index c, daily from 16 May to 4 November 2024. Lower… — Figure 1. Upper panel: the Polymarket probability that Trump wins the 2024 presidency (the conditioning leg b), the probability that a Republican wins both the popular vote and the presidency (the joint leg q), and their ratio, the conditional index c, daily from 16 May to 4 November 2024. Lower panel: the funding rate of a perpetual on c from Proposition 2 with the calibrated σc = 2.72, σb = 1.31 and ρ = 0.20, split into the base identity evaluated at c and the correlation correction; the dashed line is their sum. The correction is positive throughout and exceeds the base term in absolute value on 50 percent of the days.

The ratio's sensitivity to its legs grows without bound as the conditioning price nears zero. We find that the funding rate and its correction stay bounded through that limit. What breaks is the mark. An index backed out of two quoted legs carries a half-spread of (s_q + c s_b)/P(B), and the division makes it unquotable as P(B) falls. Table 3 gives the consequence. At half a tick per leg, the lowest conditioning probability at which a venue could quote the index within a five-cent tolerance is 0.148. At the effective half-spread of about a cent that Dubach (2026) measures on Polymarket's tape, that floor is 0.296. Margin moves the same way once each leg carries tick noise. The one-day 99 percent loss on a unit position rises from 0.083 at P(B) = 0.5 to 0.48 at P(B) = 0.01.

Only one conditioning leg in our data went to zero, and Figure 3 shows it. Biden's 2024 nomination market fell from 0.29 to zero on 22 July in a single day, after three weeks in which the joint market on Trump and Biden both being nominated traded above the Biden leg itself. That happened on 29 of 189 days, by up to 14 cents, so the ratio exceeded one and no logit volatility can be estimated for it. A floor at the levels above would have closed the contract before the jump, and the jump itself is a roll.

Figure 3. Upper panel: the Polymarket probability that Biden wins the 2024 Democratic nomination (the conditioning leg b), the probability that Trump and Biden both win their nominations (the joint leg q), their ratio, the conditional index c, and Trump's own nomination price, which c should track… — Figure 3. Upper panel: the Polymarket probability that Biden wins the 2024 Democratic nomination (the conditioning leg b), the probability that Trump and Biden both win their nominations (the joint leg q), their ratio, the conditional index c, and Trump's own nomination price, which c should track, daily from 1 May to 22 July 2024; the ratio exceeds one whenever the joint market trades above its conditioning leg, and the leg's fall to zero on 22 July is the jump at the right edge. Lower panel: the joint leg minus the conditioning leg in cents, coloured where it is positive, and the implied half-spread on the index from Proposition 4 at half a tick per leg.

Options on the conditional index are priced by the base pricer with no change when the option is void if B fails, and with one drift term when it is cash-settled. Table 2 shows how little the two conventions differ.

The basket and its margin

For a basket on several events, funding is the weighted sum of the legs' single-market identities. Correlation enters only the margin, and that is where the base case's grid is weakest, since it charges every event's adverse move at once with one dimension per event. We compare the grid against the most probable stress, found by minimising the rate function of the seven-dimensional logit diffusion calibrated to the seven 2024 swing-state markets, whose logit innovations have a mean pairwise correlation of 0.38.

Figure 4 shows what the two methods do. For an equal-weight long basket the most probable stress moves every state down together, while the grid corner moves each by the full ten points. For a long Pennsylvania, short Michigan spread the stress moves the two legs apart by 5.7 and 4.0 points and leaves the others close to zero, while the grid moves them apart by ten points each. Table 6 puts numbers on the difference. At a matched 99 percent one-day shock the grid charges 1.48 times the stress margin on the long basket, 1.80 times on the spread and 1.58 times on a covered-call book. With the base case's fixed ten-point shocks the ratios to the simulated 99 percent loss are 3.7, 4.6 and 6.2. The stress margin itself matched the simulated quantile, 0.0272 against 0.0272 for the one-day long basket. Under equal correlation the overcharge has a closed form, √(K/(1+(K-1)ρ)) for the basket and √(2/(1-ρ)) for the spread, and Figure 5 plots both against the exact book loss as the correlation varies.

Figure 4. Shock to each state's probability in the margin scenario, five-day horizon, 99 percent. Left: the equal-weight long basket, where the most probable stress moves every state down together and the grid corner moves each by the full ten points. Right: the long Pennsylvania, short Michigan… — Figure 4. Shock to each state's probability in the margin scenario, five-day horizon, 99 percent. Left: the equal-weight long basket, where the most probable stress moves every state down together and the grid corner moves each by the full ten points. Right: the long Pennsylvania, short Michigan spread, where the stress moves the two legs apart by 5.7 and 4.0 points and leaves the others close to zero, and the grid corner moves them apart by ten points each.

Figure 5. Ratio of the grid's combination rule to the most probable stress margin, one-day horizon, 99 percent, seven legs at probability one half with the mean estimated volatility, as the common pairwise correlation varies. Solid lines: the exact book loss; dashed: the closed forms √7/(1+6ρ) for… — Figure 5. Ratio of the grid's combination rule to the most probable stress margin, one-day horizon, 99 percent, seven legs at probability one half with the mean estimated volatility, as the common pairwise correlation varies. Solid lines: the exact book loss; dashed: the closed forms √7/(1+6ρ) for the long basket and √2/(1-ρ) for the spread. Log scale.

What we did not see

The path we did not see is a conditioning event that declines slowly to a few percent while both legs keep trading. The sweep of Section 4.4 models that path, and the one decline we found in 2024 was a jump. Whether a venue would keep quoting both legs through a slow decline is a question of market making, and we leave it open.

Who this is for: Researchers and quants working on prediction-market derivatives, along with investors and journalists who follow those venues.

Figures

Figure 2. Left: one-day 99 percent margin on a unit long conditional perpetual as the conditioning probability falls (log scale, falling to the right): the base-case level grid applied to the two legs, the model's own quantile, which equals the most probable stress in logit coordinates, and the… — Figure 2. Left: one-day 99 percent margin on a unit long conditional perpetual as the conditioning probability falls (log scale, falling to the right): the base-case level grid applied to the two legs, the model's own quantile, which equals the most probable stress in logit coordinates, and the quantile once each leg carries half-cent tick noise. Right: the funding rate and its correlation correction, both bounded, against the implied half-spread on the index, which is not.

Tables

Table 1. the seven variants and what each inherits from the base case.
variant	tracked quantity	funding	option pricer	margin	where
conditional	P(A \| B)	base identity in c plus ρσcσb c(1-c)(1-b)	base pricer under QB; one drift term under Q	bounded in logit shocks; the mark is not	Section 4
basket	Σk wk pk	Σk wk f(pk, σk)	simulation; no closed form	most probable stress on the joint diffusion	Section 5
spread	p1 - p2	basket with w = (1, -1)	basket	basket; the grid's worst case	Sections 5, 6
variance	realised variance of ℓ or of p	none (settles at T)	σ² T; a time integral of the base pricer	not treated	Section 6
entropy	H(pT')	none	base pricer with a concave payoff	not treated	Section 6
funding-only	∫ fdt	the contract	one quadrature	not treated	Section 6
expiring markets	p(n)t, rolled	base identity within each market	base pricer	base grid	Section 6

Table 2. European calls on the conditional index under the two settlement conventions, presidential pair, c0 = 0.481, b0 = 0.488, σc = 2.72, σb = 1.31, ρ = 0.20; prices in index points per unit notional.
T'	K	void if B fails	cash-settled	difference
1 month	0.3	0.1927	0.1873	-0.0054
1 month	0.4	0.1187	0.1142	-0.0045
1 month	0.5	0.0626	0.0592	-0.0034
1 month	0.6	0.0264	0.0251	-0.0013
1 month	0.7	0.0083	0.0077	-0.0006
3 months	0.3	0.2165	0.2045	-0.0120
3 months	0.4	0.1512	0.1415	-0.0097
3 months	0.5	0.1002	0.0915	-0.0087
3 months	0.6	0.0596	0.0543	-0.0053
3 months	0.7	0.0294	0.0268	-0.0026

Table 3. the half-spread on the conditional index and the listing floor of Proposition 4 at three half-spreads per leg, c = 0.481. Dubach (2026) supplies the spread measurements; the floor is the smallest conditioning probability at which a venue can quote the index within the stated tolerance.
half-spread per leg	what it is	index half-spread at b = 0.5	at b = 0.1	floor, 5-cent tolerance	floor, 10-cent tolerance
0.5 cents	half a tick	1.5 cents	7.4 cents	0.148	0.074
1.0 cent	effective spread paid, 2026	3.0 cents	14.8 cents	0.296	0.148
1.9 cents	median quoted spread, live markets, 2026	5.6 cents	28.1 cents	0.563	0.281

Table 4. the conditional contract as the conditioning probability falls, at c0 = 0.481, σc = 2.72, σb = 1.31, ρ = 0.20, one-day horizon, half-tick 0.005. Funding in index points per year per unit; margins in index points per unit long.
b0	funding, total	correction	implied half-spread	grid on the legs	feasible corners	model and logit stress, 99%	with tick noise, 99%
0.50	0.123	0.087	0.015	0.247	49	0.082	0.083
0.30	0.158	0.122	0.025	0.370	48	0.082	0.086
0.20	0.175	0.140	0.037	0.327	37	0.082	0.090
0.10	0.192	0.157	0.074	0.341	23	0.082	0.108
0.05	0.201	0.166	0.148	0.454	17	0.082	0.154
0.03	0.205	0.169	0.247	0.370	10	0.082	0.217
0.02	0.206	0.171	0.370	0.401	10	0.082	0.295
0.01	0.208	0.173	0.741	0.437	10	0.082	0.481

Table 5. the three nested Polymarket pairs. Days are daily logit increments; the windows are 16 May to 4 November 2024, 14 January to 21 July 2024 and 12 July to 4 November 2024. The correction and the base term are the two parts of Proposition 2 averaged along the realised path, per year per unit notional. On the nomination pair the conditional index sat within a few cents of one and crossed it on 29 days, so its logit volatility and correlation are not estimable.
pair	joint leg q	conditioning leg b	days	b range	c range	σc	σb	ρ	correction, mean per year	base term, mean abs.	days q > b
presidential	Republican wins popular vote and presidency	Trump wins presidency	172	0.44 to 0.71	0.40 to 0.82	2.72	1.31	0.20	0.076	0.116	0
nomination	Trump and Biden both nominated	Biden nominated	189	0.13 to 0.91	0.90 to 1.37	not estimable	5.43	not estimable	not estimable	not estimable	29
sweep	Trump wins every swing state	Republican wins Pennsylvania	115	0.42 to 0.67	0.28 to 0.89	4.54	1.76	-0.13	-0.117	0.563	0

Table 6. margins per unit of book, seven swing-state markets at their 1 October 2024 probabilities and estimated covariance. The matched grid sets each event's shock to its own 99 percent h-day logit move; the most probable stress is the largest loss on the 99 percent ellipsoid of the joint logit diffusion; the reference is the 99 percent loss over 400,000 simulated paths. The grid as written uses the base case's shocks of ten points and volatility multipliers up to two.
book	h	grid as written	matched grid	most probable stress	simulated 99%	matched / stress	grid / simulated
long basket	1 day	0.100	0.0401	0.0272	0.0272	1.48	3.68
long basket	5 days	0.100	0.0893	0.0607	0.0604	1.47	1.66
spread PA-MI	1 day	0.200	0.0782	0.0434	0.0434	1.80	4.61
spread PA-MI	5 days	0.200	0.1755	0.0973	0.0968	1.81	2.07
covered basket	1 day	0.0938	0.0232	0.0147	0.0151	1.58	6.21
covered basket	5 days	0.0938	0.0590	0.0369	0.0382	1.60	2.45

Abstract

Majumdar (2026a) built a perpetual future and options on a single binary prediction market from three parts: a funding-rate identity that holds the perpetual's mark on the market's probability index, a logit-normal pricer for European options on that index, and a scenario-grid portfolio margin. Nechepurenko (2026b) classified the contracts that can be written on more than one market and proved, for each, a qualitative result; none of them is priced there. We price them. The conditional index $P(A|B)$ is a martingale under the measure conditioned on $B$, and under the pricing measure it drifts. In a bivariate logit model the drift is $-\rho\sigma_c\sigma_b c(1-c)(1-b)$, so the funding rate of a perpetual on it is the single-market identity plus a correction of that size and the opposite sign. On the two nested Polymarket pairs from 2024 that we could calibrate, the correction was a sixth of the base term on one and the larger of the two on half the days on the other. It stays bounded as the conditioning probability falls to zero. What breaks is the mark: an index backed out of two quoted legs carries a half-spread of $(s_q + c\,s_b)/P(B)$, and the one-day 99 percent loss on a unit position rises from 0.083 at $P(B) = 0.5$ to 0.48 at $P(B) = 0.01$. At half a tick per leg the listing floor for a five-cent tolerance is 0.15; at the effective half-spread of about a cent measured on Polymarket's tape it is 0.30. On the one pair whose conditioning leg did fall to zero, Biden's 2024 nomination, the joint market traded above its own conditioning leg on 29 of 189 days, by up to 14 cents, and the leg went from 0.29 to zero in one day. Options on the conditional index are priced by the single-market pricer verbatim when the option is void if $B$ fails, and with one drift term otherwise. For the basket, funding is the weighted sum of the legs' identities. Correlation enters only the margin, and there we compare the one-dimension-per-event grid against the most probable stress found by minimising the rate function of the seven-dimensional logit diffusion, calibrated to the seven 2024 swing-state markets, whose logit innovations have a mean pairwise correlation of 0.38. At a matched 99 percent one-day shock the grid charges 1.48 times the stress margin on a long basket, 1.80 times on a long-short spread and 1.58 times on a covered-call book; with the fixed ten-point shocks of the base case the ratios to the simulated 99 percent loss are 3.7, 4.6 and 6.2. Under equal correlation the gap is $\sqrt{K/(1+(K-1)\rho)}$ for the basket and $\sqrt{2/(1-\rho)}$ for the spread.

Keywords: prediction markets, event-linked perpetual futures, funding rate, conditional probability, basket contracts, correlation, portfolio margin, large deviations, Polymarket

How to cite

Majumdar, A. (2026). Conditional and Basket Event-Linked Perpetual Futures: Funding Rates, Pricing and Correlation-Aware Margin. SSRN Working Paper No. 7646159. https://ssrn.com/abstract=7646159

@techreport{majumdar_a_taxonomy_of_event_linked_perpetual_futures_variant_designs_beyond_the_single_m,
  author={Majumdar, Anirban},
  title={Conditional and Basket Event-Linked Perpetual Futures: Funding Rates, Pricing and Correlation-Aware Margin},
  institution={SSRN},
  number={7646159},
  year={2026},
  url={https://ssrn.com/abstract=7646159}}

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Conditional and Basket Event-Linked Perpetual Futures: Funding Rates, Pricing and Correlation-Aware Margin