Equity Indices

Oracle Methodology for Equity Indices

External Coverage

The relayer derives external prices for equity indices from two sources:

• Spot index values during the cash session (9:30 AM – 4:00 PM ET, Monday through Friday).

• Traditional dated equity index futures quotes from institutional liquidity providers, available nearly 23/5.

Together, these sources enable the Relayer to derive external pricing 23/5, from Sunday 6:00 PM ET through Friday 5:00 PM ET, with daily gaps from 5:00–6:00 PM ET.

External Price Derivation

For equity indices such as XYZ100, the relayer consumes executable quotes for both the underlying spot index and the corresponding traditional (dated) equity index futures from institutional liquidity providers. During the cash session, the spot index value is used directly as the oracle price. Outside the cash session, the futures price is discounted to an implied spot value using an empirically observed discount rate. This two-source design eliminates the need for a manually set discount rate.

Cash Session

During the cash session, the spot index value serves as the oracle price. Simultaneously, the relayer observes the spot–futures basis and derives the implied annualized net discount rate:

$$d_t = \frac{1}{T_t} \ln\left(\frac{F_t}{S_t}\right)$$

where $F_t$​ is the concurrent futures price, $S_t$​ is the spot index value, and $T_t$​ is the time to futures settlement in years. The net discount rate $d = r-q$ implicitly captures the prevailing interest rate $r$ and forward dividend yield $q$ without requiring either to be specified independently.

The relayer maintains a continuous-time exponentially weighted moving average of $d_t$ with a time constant $\tau = 1$ hour:

$$\bar{d}_t = \beta_t, \bar{d}_{t^-} + (1 - \beta_t) d_t, \qquad \beta_t = e^{-\Delta t / \tau}$$

where $\Delta t = t - t_{\text{prev}}$​ is the elapsed time since the prior update. As a protective measure, each EMA update is clamped such that $|\bar{d}_t - \bar{d}_{t^-}| \leq 0.01\text{ bps}$, ensuring no single observation produces a disproportionate rate adjustment.

Extended Session

Outside the cash session — but within futures trading hours — the oracle price is derived by discounting the futures price at the prevailing EMA discount rate:

$$S_t = F_t e^{-\bar{d}_t T_t}$$

The EMA rate established during the prior cash session carries forward unchanged until the next cash session opens, at which point the EMA resumes updating with live basis observations.

XYZ100

The XYZ U.S. 100 Index (XYZ100) tracks the value of a modified capitalization-weighted index of 100 large non-financial companies listed on a U.S. exchange.

Parameters

• Discount Rate EMA Time Constant $(\tau)$ : 1 hour

• Discount Rate EMA Clamp: 0.01 bps per update

Underlying Suffix	Active Until	Expiration
H6	2026-03-15T22:00:00Z	2026-03-20T13:30:00Z
M6	2026-06-14T22:00:00Z	2026-06-19T13:30:00Z
U6	2026-09-13T22:00:00Z	2026-09-18T13:30:00Z
Z6	2026-12-13T22:00:00Z	2026-12-18T13:30:00Z