# HF across prices — rebalancing scenario The user chose the rebalancing scenario only. This is a fixed-time estimate from the known hedge curve, anchored to current supplied assets and actual debt. It is not a projected series of executed CoW orders or a funding/borrowing approval. ## Inputs and account checks `positions.js` retains notional, strike, expiry, underlying units, IV, Aave prices and account LT/LTV from the same lens snapshot. `risk-reader.js` resolves every active collateral/borrowing reserve by its ID, reads its parameters, debt token balance and oracle price at that same block, then reconciles reconstructed collateral, debt and weighted LT/LTV against the lens. Reserve-ID holes are kept. Both debt assets matter. Borrowed base reprices with the x-axis; quote and other asset prices stay fixed. Collateral eligibility flags are respected. Aave E-mode, unreconciled balances or missing inputs make the chart unavailable while leaving the position card available. A final block-hash check rejects a reorg during the model read. Scope: Base V3 and variable debt, matching the current pair interface. Sources: `thetaAaveCattle/src/interfaces/IAavePool.sol`, the pair and lens; [Aave IPool](https://github.com/aave/aave-v3-origin/blob/main/src/contracts/interfaces/IPool.sol). The additional reads are read-only and do not affect indexer coverage. ## Hedge curve and value Let `s` be base price in quote tokens, `K` strike, `N` fixed strategy notional, and `C(s)` the zero-rate Black–Scholes call value at fixed IV and time. Time is quantized at the contract's next one-hour epoch boundary. ```text Long target base b(s) = N Φ(d1) Short target base b(s) = N [1 − Φ(d1)] Long value V(s) = V(s0) + N [C(s) − C(s0)] Short value V(s) = V(s0) + N [s − s0 − C(s) + C(s0)] Quote holdings q(s) = V(s) − s b(s) ``` `V(s0)` comes from current holdings valued in quote units. The hypothetical initial rebalance preserves that value. It may change weighted collateral when the two reserves have different liquidation thresholds. Consequently, the curve at today's price is labelled **after model rebalancing**; actual account HF stays in the account grid above it. The x-axis current price uses the Aave base/quote price ratio. The quote token is not assumed to be worth exactly one USD. This conserves value; setting quote holdings to `(N−b)×K` would not. The formulas above apply while the target is affordable. The chart models a **one-way price move from today**, with no extra borrowing to finance trades. ### When quote assets run out The first implementation stopped the curve when ideal quote holdings became negative. The user correctly identified that as an execution funding limit, not undefined HF: wstETH collateral can continue appreciating against USDC debt. If the initial target is affordable, follow the self-financing path until quote holdings reach zero at `sf`. Beyond that boundary, in the direction where the target requires more buying, keep `Bf = b(sf)` base and zero quote. Value becomes `Bf × s`; existing debt continues to reprice. This affects long on an increasing price path and short on a decreasing price path. No negative cash or new debt is introduced. With quote-only debt, HF can continue growing without a ceiling as base price increases under the fixed assumptions. Base-denominated debt can instead give HF a finite upper limit. If today's target is already unaffordable, start with `B0 = V(s0)/s0` base and zero quote. Keep those holdings until the target decreases to `B0` at a join price `sj`. Reanchor the hedge integral at that point: ```text F(s) = N C(s) for long; N [s − C(s)] for short V(s) = B0 sj + F(s) − F(sj) q(s) = V(s) − s b(s) ``` Reusing the original negative-cash integral would assume an unfunded initial trade. The implementation instead solves the affordable join using the target delta and evaluates quote as a stable difference of `N K Φ(d2)` values. Holdings, value, HF and borrowing capacity remain continuous at both kinds of boundary. A price reversal after quote exhaustion would follow a different path; this chart does not model that history. Expiry processing, zero IV and absent funded holdings remain outside this continuous scenario. Spread earnings, interest, fees, slippage, discrete grid steps and execution delays are excluded. ## Risk lines For each eligible supplied asset, let `t` be LT and `l` be LTV as fractions. ```text C = Σ supplied × price W = Σ supplied × price × t A = Σ supplied × price × l D = Σ debt × price HF = W / D Actual LTV = D / C LTV limit = A / C Borrowing line in HF units = W / A ``` Liquidation is marked at HF 1. The borrowing boundary is `D=A`; it is not a fixed LTV percentage placed on an HF axis. Caps, liquidity and further Aave restrictions can limit borrowing before this boundary. The chart does not certify outgoing trade settlement. No debt has no finite HF or liquidation price. Borrow and repay scenarios modify only the selected debt quantity, starting from the current snapshot each time. Borrowed proceeds remain outside the position; repayment funds come from outside it. Over-repayment is refused. Current account figures, wallet identity and supplied collateral remain the actual snapshot. ## Curves and crossings The shape follows strategy, reserve weights and debt mix. It is not selected by a long/short label. The fictional long example uses 0.25 wstETH + 220 USDC debt and has a U-shaped HF curve. The fictional short uses USDC debt and bends downward toward liquidation as price falls. The current live long's USDC-only debt produces a different curve. Samples include consistent synthetic account and reserve data. Uniform plot samples alone can miss two crossings around a shallow minimum. `risk-model.js` finds stationary points before bracketing crossings. Since debt is affine in price, the HF slope numerator has derivative `W''D`. `W''` and `A''` change sign at the analytic log-price inflection derived from their reserve weights. The search splits at those points, finds extrema, then brackets both sides of HF 1 and the borrowing boundary. Funding joins are also explicit search and plot boundaries: a join can be a local extremum with a discontinuous slope. Derivative searches use the appropriate one-sided derivative at each join. On the segment with no quote left, base holdings stay constant, HF is fractional linear and the borrowing-limit difference is affine in price. Independent Astra review verified this fix. The regression has a true minimum below HF 1 while all 161 ordinary samples sit above 1, and still finds both roots. Other tests cover reference BS values, self-financing trades, debt repricing, borrow/repay isolation, reserve flags and account reconciliation. The funding correction is compared with 20,000 separately executed affordable trades for each price direction, for long and short, including initially underfunded targets. Tests also check boundary continuity, quote-only HF growth, the base-debt asymptote, and liquidation/borrowing crossings after quote exhaustion. ## Identity and future flows Position titles show `notional / baseUnit`, rounded with an approximation marker, and distinguish it from a leverage multiple. Current configuration encodes long call-like and covered-short modes, not a separate Call/Put subtype. Borrowed base can change net exposure without changing that encoded strategy. Put naming must not be inferred from debt mix alone. Borrowing follows deployment and funding as a separate owner decision. See [ROLL-PLAN.md](ROLL-PLAN.md) for the studied destination-review and activation flow.