The Yield-Aware Funding Mechanism

A perpetual's funding rate is its most critical mechanism, ensuring the derivative remains tethered to its underlying index. Nunchi's funding mechanism is uniquely yield-aware, engineered to transparently price the inherent "cost of carry" for a new generation of rate-based and basis-based instruments.

The Universal Funding Formula

All perpetual markets on Nunchi use a single, robust funding formula. The funding rate that is settled between longs and shorts is composed of two primary components: a Premium Component and an Interest Rate "Carry" Component.

1. The Premium Component: This is the standard component found in all perpetuals. It measures the deviation of the perpetual's traded mark price from the oracle index price. If the mark price is higher than the index, longs pay shorts, and vice versa. This forces the perpetual to track its benchmark closely.

2. The Interest Rate "Carry" Component: This is our key innovation for yield-bearing instruments. It is defined as the difference between the annualized yield of the base asset (rbase) and the quote asset (rquote). This term ensures that participants are correctly and fairly compensated for the native yield they are synthetically exposed to.

Our dual-primitive system (Yield Perps and Basis Perps) manifest how this universal formula applies differently to each, based on the specific definition of its r_base and r_quote.

Applying the Formula: YPs vs. BPs

The key to understanding our funding mechanism is to correctly identify the "base" and "quote" assets for each perpetual type.

Perpetual Type	What it Tracks	r_base (Yield of Base Asset)	r_quote (Yield of Quote Asset)	Resulting Carry Term
Yield Perp (e.g., T-Bill Yield)	An annualized rate (APY/APR)	0%. The instrument tracks the yield itself; the yield does not have a further yield.	0%. The quote asset is typically a non-yielding stablecoin like USDC.	0%. Funding is driven entirely by the Premium component.
Basis Perp (e.g., stETH/ETH)	A price ratio between two assets	The staking APR of the base asset (stETH).	The staking APR of the quote asset (ETH), which is typically 0%.	stETH APR - 0%. The carry term is essential and non-zero.

Example Walkthroughs:

• For a T-Bill Yield Perp: The instrument's value is the rate. There is no underlying asset that generates a further yield. Therefore, r_base = 0 and r_quote = 0. The funding is purely Premium = r_index - P_perp, where r_index is the oracle APY and P_perp is the traded APY. This mechanism forces the traded rate to align with the true on-chain rate.

• For an stETH/ETH Basis Perp: The r_base is the ~3.5% staking yield of stETH. A long position holder is synthetically exposed to the stETH/ETH price ratio but is not receiving the actual staking rewards. Therefore, they must pay this 3.5% carry component to the short holder, who is presumably hedging by holding real stETH and collecting those rewards. This is economically sound and creates a fair, balanced market.

Advanced Mechanics: Skew-Based Adjustment & Real-Time Payments

To ensure market stability and prevent persistent imbalances, we incorporate two further enhancements:

• Skew-Based Dynamic Funding: If a market becomes heavily one-sided (e.g., too many longs), a beta term is added to the funding formula. This term, proportional to the long/short open interest ratio, accelerates the funding rate, making it more expensive to hold a position on the crowded side. This encourages arbitrageurs to step in and rebalance the market.

• High-Frequency Funding Payments: By building on a high-performance chain, Nunchi can settle funding payments in near real-time (e.g., every minute or even every block), rather than every 8 hours. This continuous settlement process reduces the risk of large divergences between the perpetual and the index, creating a smoother and more dynamic market for all participants.