Editing Openai/6973721c-28b0-8007-a991-09211709d274 (section)

==== 2) “Optimal LTV” calculation (practical framework) ====

There isn’t one universal optimum because it depends on:
* oracle type + update frequency
* liquidation bonus / close factor / auction mechanics
* PT liquidity + slippage under stress
* your rebalance frequency (do you monitor hourly, daily, weekly?)
* borrow rate volatility (util shock probability)

So the right way is: choose an acceptable liquidation probability over a horizon and back out a safe LTV.

===== Step 1 — Define variables (per market) =====
* LLTV (Morpho) or LT (Euler equivalent trigger)
* h = risk horizon (e.g., 1 day if you monitor actively; 7 days if you want “sleep well”)
* σ = volatility of collateral value in loan terms (PT priced in borrowed asset)
* r_b = borrow APR (use a stressed value, not today’s)
* LB = liquidation bonus / penalty (how much collateral you lose when liquidated)
* s = stress slippage haircut for unwinds (PT liquidity + DEX depth)
* z = quantile (e.g., 2.33 for 99%, 3.09 for 99.9%)

===== Step 2 — Compute a conservative “survival buffer” =====

Two things push LTV up over horizon h:
# collateral value can drop
# debt grows via interest

A simple (usable) bound:
* Collateral shock factor:

q=exp⁡(−z⋅σh)q = \exp(-z \cdot \sigma \sqrt{h})q=exp(−z⋅σh)
* Debt growth factor:

g=exp⁡(rb⋅h)g = \exp(r_b \cdot h)g=exp(rb⋅h)
* Execution haircut for liquidation mechanics + slippage (rule of thumb):

η=1−(LB+s)\eta = 1 - (LB + s)η=1−(LB+s)
(If LB=7% and you assume 5% slippage in stress, η≈0.88\eta \approx 0.88η≈0.88)

===== Step 3 — Safe initial LTV =====

For Morpho Blue, you want to stay below LLTV even after shocks:

LTV0,max⁡≈LLTV⋅qg⋅η\textbf{LTV}_{0,\max} \approx LLTV \cdot \frac{q}{g} \cdot \etaLTV0,max≈LLTV⋅gq⋅η
This gives you an LTV that has roughly “(1 − tail probability)” chance of staying solvent over horizon h, under your σ/r assumptions, and acknowledges that liquidation is lossy.