Physical settlement

Definition

Physical settlement is the maturity outcome when the final observed price is below the barrier. COUPON holders redeem Stock Tokens instead of USDG; SHIELD holders receive the COUPON escrow in USDG and give up their Stock Tokens. Nothing is bought or sold on a market: the escrowed assets change hands at the initial level s0.

Formula

fact For N_c matched COUPON notional in quote units (USDG has 6 decimals; read decimals() at construction, never hard-coded):

stockOut = N_c × 10^(18 − quoteDecimals) × 1e8 / s0

Equivalently: notional in USDG divided by s0 in USDG, expressed in 18-decimal Stock Token units. The division rounds down on redemption while the matched stock was rounded up at strike, so a few wei of Stock Token dust can remain in escrow after every unit is redeemed. Dust is not swept as fees (sweepFees moves only USDG accruedFees); it simply stays in the contract.

Worked arithmetic

illustrative N_c = 100,000 USDG = 100,000 × 1e6 = 1e11 quote units. s0 = 180.00 = 180 × 1e8 = 1.8e10.

stockOut = 1e11 × 1e12 × 1e8 / 1.8e10 = 1e31 / 1.8e10 = 555,555,555,555,555,555,555 wei (floor, on redemption) = 555.555555555555555555 NVDA Stock Tokens stockMatched at strike = ceil(same) = 555,555,555,555,555,555,556 wei

Per COUPON unit (1 USDG): 1e6 × 1e12 × 1e8 / 1.8e10 = 5,555,555,555,555,555 wei ≈ 0.005556 tokens, i.e. 1 / 180 of a token.

If the final price is 99.00, those tokens are worth 555.5556 × 99.00 = 55,000.00 USDG. The COUPON holder’s principal loss is 45,000 USDG (45%), partly offset by coupons earned before the breach.

Who gets what

Party	Gives	Receives
COUPON holder (per unit)	1 unit burnt	1e6 × 1e12 × 1e8 / s0 Stock Token wei; no coupon for the maturity observation
SHIELD holder (per unit)	Its matched Stock Tokens (already in escrow)	1 USDG from the COUPON escrow, plus unused coupon prefund
Protocol	—	Accrued USDG fees (rounding dust of stock stays in escrow, unowned)

Why settle physically

1. No price impact. The protocol never has to sell stock into a falling market; it transfers tokens already in escrow.
2. No oracle dependence for the amount. The amount of stock is fixed by s0 at strike, not by the maturity price. The maturity price is only used for the binary barrier test.
3. Issuer neutrality. Stock Tokens are debt securities of the issuer; physical settlement redistributes existing tokens rather than creating synthetic exposure.

ERC-8056 multiplier

fact Stock Tokens expose uiMultiplier(); the feed price already reflects it (Robinhood building guide). Settlement moves raw ERC-20 balances. A holder’s wallet may display balanceOfUI, which is the raw balance scaled by the multiplier; the protocol’s arithmetic is in raw units throughout and never applies the multiplier itself.

Redeeming

After status Matured, redeem(seriesId, units) burns COUPON units and transfers Stock Tokens, and redeemShield(seriesId, units) burns SHIELD units and transfers USDG plus unused prefund. Redemption is pull-based and has no deadline. See Series lifecycle.