Aave Borrow Rate Perpetual (AAVEBORROW)

This perpetual contract is designed to replicate the cumulative borrowing cost of a reference Aave variable-rate loan, allowing traders to hedge interest rate risk or speculate on DeFi borrow conditions.

Characteristic	Description
What it Tracks	The cumulative interest accrual of a variable-rate loan on Aave, represented by a Borrow Multiplier Index.
Index Definition	A Borrow Multiplier Index, Jt, that grows based on the instantaneous Aave borrow rate, rt. It is defined as: where Y is the number of seconds in a year. This index represents the total growth factor of a loan's principal due to interest.
Oracle Type	A 24/7 on-chain oracle that reads the live variable borrow rate for a given asset directly from the Aave v2/v3 protocol pools or uses a smoothed nowcast of this rate.
Market Type	Cash-Settled Index Perpetual.
PnL Formula	The PnL for a position with notional N is designed to perfectly match the interest accrued on an Aave loan of the same initial notional. The infinitesimal PnL is given by PnLt = NdJt. Over a period [0, T], the total PnL is: • PNL (Long) = N x (JT - 1) • PNL (Short) = N x (1 - JT) Where: • N: The USD notional value of your position. • JT: The value of the Borrow Multiplier Index at the end of the period.
Use Cases	Hedging (Long): • Borrowers on Aave can take a long position of the same notional value to perfectly neutralize the variable interest cost of their loan. Directional Trades: • Go long to speculate on rising Aave borrow rates (e.g., during periods of high utilization). • Go short to speculate on falling Aave borrow rates. Arbitrage: • Trade the spread between Aave borrow costs and funding rates on other perpetual exchanges.
Users	• DeFi Borrowers & Lenders • Relative-Value & Arbitrage Funds • Macro Traders speculating on on-chain rates • DAOs managing treasury debt
Vol-stat (σ)	Low-to-Medium. Aave borrow rates are generally less volatile than crypto asset prices but can experience sharp spikes during periods of high market stress and borrowing demand.
Margin Numbers	Derived from the Max Leverage tiers. For the initial leverage tier, the Initial Margin (IM) is a percentage of the notional position value (e.g., 33.3% for 3x leverage).

OraclePx

The AAVEBORROW-PERP does not track a direct external price. Instead, its price is a transformation of an internally calculated index, the Borrow Multiplier Index (J_t), which is driven by an on-chain oracle.

1. Rate Observation: At discrete moments in time, t_k, the oracle reads the instantaneous annualized borrow rate, r_k, from the target Aave pool.

2. Index Construction: This rate is used to update a Cumulative Borrow Log-Index, K_t, which integrates the rate over time.

$$K_{k+1} = K_k + \frac{r_k}{Y} \Delta t_k$$

1. The primary Borrow Multiplier Index ( is then calculated as the exponential of the log-index.

$$J_k = \exp(K_k)$$

1. This index J_t starts at J₀=1 and grows continuously, precisely mirroring how a debt balance compounds on Aave.

MarkPx

The mark price P_t of the perpetual is an affine transformation of the underlying Borrow Multiplier Index J_t. This ensures the price is always positive and complies with HIP-3's per-update constraints, while preserving a direct PnL relationship to the index.

The price is calculated using an anchored mapping:

$$P_t = B_t + S(J_t - A_t)$$

Where:

• S is a large, constant scale factor (e.g., 1,000,000) that converts small changes in the index into visible price ticks.

• B_t is a piecewise-constant baseline that keeps the contract price far from zero.

• A_t is a piecewise-constant anchor that represents the reference level for the index J_t.

Re-Anchoring Mechanism:

To prevent the price from drifting indefinitely, the system periodically re-anchors. The anchor is:

$$|\hat{J}_t - A_t|$$

If the deviation of the index from its anchor exceeds a set threshold (e.g., 0.005), the anchor and baseline are updated atomically:

$$A_t^+ = \hat{J}_t$$

$$B_t^+ = B_t^- + S(A_t^+ - A_t^-)$$

This operation recenters the mapping around the current index level while keeping the mark price P_t perfectly continuous, thus having no PnL impact on traders.

HIP-3 Price Clamping:

The raw computed price P_k at each tick is clamped to satisfy the HIP-3 1% per-update constraint. The final quantized price posted to the exchange is:

$$\bar{P}_k = \text{clamp}\left(\text{quantize}(P_k), (1-0.01)\bar{P}_{k-1}, (1+0.01)\bar{P}_{k-1}\right)$$

Any residual between the raw computed price and the final quantized price is carried forward to the next tick to ensure PnL exactness over the long run.

ExternalPerpPx

For venues that use an external price for band-limiting, the policy for the AAVEBORROW-PERP is to use its own calculated mark price as the anchor.

Band:

$$\pm \min(1/\text{maxLeverage}, 20\%)$$

Policy:

ExternalPerpPx = A slow Exponential Moving Average (EMA) of the perpetual's own mark price P_t. This provides a stable, self-referential anchor that smooths out short-term noise while ensuring the live market cannot deviate excessively from its recent history.

Worked Example

This example demonstrates how a long position in the Aave Borrow Rate Perpetual can provide a perfect, pathwise hedge against the interest costs of a variable-rate Aave loan.

1. Scenario & Initial Conditions

A DeFi protocol's treasury takes out a $5,000,000 USDC loan from Aave to fund a short-term operation. To eliminate the risk of rising interest rates, the treasury manager simultaneously opens a long position in the AAVEBORROW-PERP.

• Aave Loan Initial Notional D₀: $5,000,000

• Perpetual Position Notional N: $5,000,000 (long)

• Time Horizon T: 30 days

• Aave Borrow Rate r_t: For simplicity, we assume the Aave variable borrow rate remains constant at 6% APR for the 30-day period.

At the start of the hedge t=0:

• The perpetual's Borrow Multiplier Index is initialized at J₀ = 1.

• The perpetual's pricing parameters are:

  • Scale Factor S: 1,000,000

  • Anchor A₀: 1

  • Baseline B₀: 20,000

2. Calculating the Aave Loan Interest Cost

First, we calculate the total interest that will accrue on the Aave loan over 30 days. The debt balance on Aave grows according to the Borrow Multiplier Index, J_t.

The value of the index after 30 days T is:

$$J_T = \exp\left(\int_0^T \frac{r_s}{Y} ds\right)$$

With a constant rate r_t = 0.06 and a 30-day period (T = 30 x 86400 = 2,592,000 seconds):

$$J_T = \exp\left(\frac{0.06}{31,536,000} \times 2,592,000\right)$$

$$J_T = \exp(0.0049315...) \approx 1.0049437$$

The total interest accrued on the loan ΔD_T is the difference between the final and initial debt balances:

$$\Delta D_T = D_T - D_0 = D_0(J_T - 1)$$

$$\Delta D_T = \$5,000,000 \times (1.0049437 - 1)$$

$$\Delta D_T = \$5,000,000 \times 0.0049437 = \$24,718.50$$

Over 30 days, the treasury owes $24,718.50 in interest to Aave.

3. Calculating the Perpetual's Mark-to-Market PnL

Next, we calculate the PnL generated by the long AAVEBORROW-PERP position over the same 30-day period. The PnL is determined by the change in the same Borrow Multiplier Index, J_t.

The cumulative PnL for a long position is given by the formula:

$$\text{PnL}_T = N(J_T - 1)$$

Using the same notional N = $5,000,000 and the final index value J_T ≈ 1.0049437:

$$\text{PnL}_T = \$5,000,000 \times (1.0049437 - 1)$$

$$\text{PnL}_T = \$5,000,000 \times 0.0049437 = \$24,718.50$$

The long perpetual position generated a profit of $24,718.50.

(Note on Price: The actual mark price of the contract would also change. The initial price was:

$$P_0 = 20000 + 1,000,000 \times (1-1) = 20,000$$

The final price would be:

$$P_T = 20000 + 1,000,000 \times (1.0049437 - 1) = 20000 + 4943.7 = 24,943.70$$

The PnL comes from this mark-to-market gain.

4. Conclusion: The Perfect Hedge

We can now assess the net financial impact on the treasury.

• Cost (Interest Paid to Aave): -$24,718.50

• Gain (PnL from Long Perpetual): +$24,718.50

• Net Borrowing Cost: $0.00

By opening a long AAVEBORROW-PERP position with a notional equal to its loan principal, the treasury perfectly neutralized its borrowing cost. The mark-to-market profit from the perpetual contract grew in lockstep with the interest accruing on the Aave debt, demonstrating the instrument's power as an exact, pathwise hedging tool.