How an Index Is Built

A prediction market prices a future value: where CPI will print, what a company will be worth at its IPO. A perpetual future needs a current price. The Mecone index is the bridge between the two, built in four steps.

1. From bets to a probability distribution

A market that trades discrete outcome bins (“CPI between 3.6% and 3.8%”, “valuation above $900B”) carries more information than a single price: the whole set of bin prices is the crowd’s probability distribution over the outcome. Raw prices, however, include the venue’s margin (the vig): summed probabilities exceed 1. We first strip it,

recovering an arbitrage-free probability mass function $q$ over the outcome bins (threshold-style markets are first converted to bin masses through their survival function). The result is the crowd-implied distribution for the next release.

2. From the future to the present: the barycenter glide

The distribution above describes the value at expiry. To quote a price now, we interpolate between the last official print $p$ (a point we know) and the crowd’s forward view $q_t$ (a distribution that updates every second), using the Wasserstein barycenter from optimal transport. In one dimension it has a closed form: the barycenter’s quantile function is the weighted average of the endpoints’ quantile functions,

where $t \in [0,1]$ advances over the release cycle. Reducing to the mean gives the published index in its simplest form,

an anchored glide: the index starts at the last official print and converges to the crowd’s expectation as the next print approaches. Computation is stateless (open-loop): the index never consumes its own prior output, so it cannot feed back on itself.

3. From an index to a perp: mark and funding

A perpetual contract quotes two numbers against the index. The oracle price is the index itself; the mark follows trading. Funding periodically transfers the premium between longs and shorts,

pulling the mark back toward the index. Because the index is derived from the prediction market, arbitraging that premium routes volume back into the underlying market, which deepens the book that the index is derived from.

4. Why it is hard to manipulate

• Depth is the cost. The index reads an aggregated order book; moving it requires walking real resting depth, and we measure the dollar cost to move each index (the cost-to-move, published per index to licensees).
• Persistence is required. Values are persisted to an immutable series on a fixed cadence; a one-shot spike must survive re-quoting market makers across snapshots to register at all.
• Robust reduction. Outlier snapshots are filtered before they reach the series, and the index is bounded by its market’s own outcome support.
• The anchor absorbs. Under the glide, a manipulator moves only the $t\,\mathbb{E}[q_t]$ term, and the final settlement is the official print itself, so a pushed basis is a mean-reverting trade with negative carry, not free profit.
• Live monitoring. Production monitoring tracks recompute jitter and fires a deviation alert on any outsized move, so an anomaly is flagged, not just diluted.