A quoted rate has three components: the spot reference, carry, and spread. The first two are what any forward costs; the third is the vault’s compensation for underwriting the residual risk.
Carry
Carry is the interest rate differential between the two currencies over the horizon. Holding dollars for 90 days earns dollar interest; holding euros earns euro interest. A forward rate has to reflect that difference, otherwise one side could earn a riskless profit by borrowing in one currency and lending in the other. The dollar leg is anchored on tokenised cash yields available on Arc; the euro leg on a published euro short-term reference. The forward before spread is
F = S × (1 + r_usd × t) / (1 + r_eur × t)
where S is the spot reference (USD per EUR), r the annualised yields and t the horizon in years.
Spread
The spread has a fixed floor, a term that grows with the horizon, and a term that grows with the epoch’s net imbalance:
spread = s0 + s_h × (days / 30) + s_i × imbalance
imbalance is the epoch’s net residual after netting, divided by the epoch cap, between 0 and 1. It is signed by direction: a lock that adds to the residual pays the full imbalance term; a lock that offsets the residual pays a reduced one, because it lowers the amount the vault has to hedge. This is what makes netting visible in the price.
Worked example
A user deposits 1,000 USDC for a 90-day lock into EURC. Illustrative inputs:
| Spot reference (USD per EUR) | 1.0800 |
| Dollar yield, annualised | 4.80% |
| Euro yield, annualised | 2.40% |
| Horizon | 90 days (t = 0.25) |
| s0 / s_h / s_i | 0.05% / 0.03% per 30 days / 0.20% |
| Epoch imbalance, same direction as the user | 0.40 |
Carry-adjusted forward:
F = 1.0800 × (1 + 0.048 × 0.25) / (1 + 0.024 × 0.25) = 1.0800 × 1.0120 / 1.0060 = 1.08644
Spread:
0.05% + 0.03% × 3 + 0.20% × 0.40 = 0.05% + 0.09% + 0.08% = 0.22%
Rate quoted to the user, USD per EUR:
R = 1.08644 × (1 + 0.0022) = 1.08883
Receipt amount:
1,000 / 1.08883 = 918.42 EURC on the settlement date
At spot the same 1,000 USDC would have bought 925.93 EUR. The difference, 7.51 EUR or about 0.81%, is the premium: roughly 0.60% carry and 0.22% spread, compounded. It is the most the user can be worse off than the spot price on the day they locked. If the euro strengthens over the 90 days the user is better off than spot at settlement; if it weakens they are worse off. Either way the receipt is worth 918.42 EURC.
Had the user’s direction offset the epoch’s residual, the imbalance term would have been reduced and the quote closer to 1.0880.