Realized variance

Realized variance is computed on-chain from the Chainlink feed's round history — by VarianceAccumulator as the window is checkpointed and finalized, by RealizedVarianceOracle for trailing windows, and by the Lens for the live "realized so far" figure that the market's projection blends in.

Sampling grid

All times are unix seconds, Δ = sampleInterval, n = (expiry − start) / Δ (must divide exactly).

tᵢ = start + i·Δ,   i = 0..n
Pᵢ = answer of the latest Chainlink round with updatedAt ≤ tᵢ   (scaled from 8 to 18 decimals)

Annualized realized variance (WAD)

rᵢ  = lnWad(Pᵢ · 1e18 / Pᵢ₋₁)            i = 1..n   (signed WAD)
RV  = Σ rᵢ² · 31_536_000 / (expiry − start)   (WAD; rᵢ² computed as rᵢ·rᵢ/1e18)
RVc = min(RV, capVariance)

RV = 1e18 is 100% annualized vol. The cap is applied to the payout, not to the measurement: finalVariance is stored uncapped and the app shows what actually happened even when it finished above the cap.

The accumulator stores sumSquaredReturns incrementally as samples are checkpointed, and realizedSoFar annualizes that partial sum over checkpointedThrough − start. Both the Lens' live figure and the market's projection read it from there rather than recomputing the window, which is why a market has to be current before it can quote. See Checkpoints and finalization.

Phase-aware Chainlink round search

A proxy round id is (phaseId << 64) | aggregatorRoundId. priceAt(t):

1. p = proxy.phaseId(); latest = proxy.latestRoundData(); hi = latest.roundId & 0xFFFFFFFFFFFFFFFF for phase p.
2. Loop over phases p, p−1, …: read first = getRoundData(p<<64 | 1). If first.updatedAt ≤ t, binary-search lo = 1..hi for the largest round with updatedAt ≤ t and return its answer. For phases below the current one, hi is found by exponential probing until the round does not exist, then bisection. Otherwise p −= 1; if p == 0 revert WindowPredatesFeed.
3. All calls are staticcalls.

A round does not exist when getRoundData reverts or returns updatedAt == 0 — verified live on Base: the OCR aggregators behind ETH/USD return zeros for unknown rounds instead of reverting (FluxAggregators revert No data present). Both are handled and tested.

The highest phase whose first round is ≤ tᵢ wins, then the largest round in that phase with updatedAt ≤ tᵢ. Sample 0 is a full search; each next sample gallops forward from the previous round — the same result as a per-sample binary search with fewer calls. Cost is O(log rounds) per sample.

Errors: WindowPredatesFeed if no round ≤ start; InvalidAnswer for answer ≤ 0; feeds with more than 18 decimals are rejected.

Why phases matter

On Base mainnet (checked 2026-09-02) ETH/USD is in phase 3, whose round 1 has updatedAt = 1787757083; phase 2 round 1 = 1773930645, phase 1 round 1 = 1691045273. Seven-day windows therefore cross the phase 2 → 3 boundary; the backend's 7d trailing window reports phases_used: [2, 3]. The fork test and demo use 5-day windows inside phase 3; phase crossings are covered by unit vectors (overlap and gap variants, three phases). The accumulator's cursor stores the phase it is in, so a window that crosses a boundary resumes correctly across bounded calls.

Off-chain replica

The backend (src/chainlink.rs) replicates the same search, dense-fetches rounds through Multicall3 and caches them in SQLite. It computes rᵢ = ln(Pᵢ/Pᵢ₋₁) and RV = Σ rᵢ² · 31 536 000 / (end − start) in f64; WAD strings are round(rv·1e18). The cap is not applied off-chain. Reference vectors in contracts/test/vectors/rv_vectors.json come from a Python Decimal(80) implementation; Solidity agrees within 1e-9 relative (actual ≤ 1e-14).