Choosing An Interest Rate Model For Lending Protocol: a Practitioner’s Framework
Most lending protocols inherit their interest rate model from the codebase they forked. This piece is a diagnostic framework for deciding whether that inherited model fits the pool, and if not, which other models would.
IR model selection as an inherited decision
When a new lending protocol launches, the interest rate model is rarely designed from scratch. In most cases it is copied from the protocol the team forked along with the parameter values that came with it. The model is treated as infrastructure rather than as a deliberate choice about how the pool will respond to its users.
The cost of this is invisible until it isn’t. What protocol teams call an interest rate model is, more precisely, a behavioral model: a set of encoded assumptions about how users respond to rate changes, how elastic their demand is, and how quickly they arbitrage external alternatives. When those assumptions match the pool’s actual user base, the model works. When they don’t, one of two failures follows: rates fail to constrain utilization at the moments it matters, allowing bad debt to accumulate; or rates overcorrect, making the pool unusable for the borrowers it was designed to serve.
This piece lays out the diagnostic questions a protocol team should answer before selecting or accepting an IR model, then maps those answers to the six models currently in production use.
Four Diagnostic Questions
Before evaluating any IR model, a protocol team should be able to answer four questions about their pool. Together, the answers narrow the field of appropriate models from six to two or three viable candidates.
- How elastically do users respond to rate changes?
Some pools are populated by sophisticated arbitrageurs who actively manage positions in response to small rate differentials. Others are populated by passive depositors and infrequent borrowers who only respond to large, sustained changes. The same model behaves very differently in these two populations. In an elastic pool, a reactive model can stabilize utilization with gentle rate changes, because users will arbitrage small mismatches back toward target. In an inelastic pool, the same model fails: users do not react to small changes, so the model must escalate rates much more aggressively to get any response, and by the time it does, utilization has already drifted far off target. Conversely, an aggressive model in an elastic pool overcorrects: rates spike on noise because the model assumes the pool needs decisive intervention, while users are already adjusting. Elasticity can be estimated empirically: how quickly does utilization revert toward target after a perturbation, and how does revert speed correlate with the magnitude of the rate change at the time? - What does this pool tolerate: IR volatility or illiquidity?
This is the central tradeoff in IR model design and the one most often inherited unconsciously. Reactive models trade rate stability for utilization control: they move rates aggressively to keep utilization near target, accepting visible IR volatility as the cost. Stable models accept some utilization drift in exchange for predictable rates. Neither preference is wrong. A protocol prioritizing capital efficiency above all - high target utilization, narrow supply-borrow spread is implicitly choosing reactivity. A protocol whose borrowers run strategies requiring rate predictability is implicitly choosing stability. The risk is inheriting a model whose preference does not match the user base. - How predictable is utilization in normal conditions?
A pool with predictable, near-target utilization is well-served by a linear kink model: the model only does meaningful work during the rare deviations from target, and its simplicity is a feature. A pool with consistently noisy utilization needs a model that absorbs noise without overreacting, either through an optimal range (Frax, Kashi) rather than a single point, or through dampened response below a critical threshold (Silo).Pool maturity matters here. New pools have unpredictable utilization not because the underlying market is volatile but because borrower and lender behavior has not yet stabilized. A model appropriate for a mature pool is often inappropriate for the same pool in its first three months. - What is the worst case the pool needs to survive?
Different models prioritize different stress scenarios. Linear models with high γ assume the worst case is sustained near 100% utilization. Silo’s dynamic model assumes the worst case is utilization above a critical threshold, and accelerates penalties the longer that condition persists. Morpho’s adaptive curve assumes the worst case is sustained mismatch, and gradually shifts the entire curve to compensate. A pool whose dominant tail risk is a sudden liquidity shock - a large lender exit, an oracle event, correlated collateral selloff needs a model that responds quickly. A pool whose tail risk is sustained off-target conditions over weeks needs a model that adjusts its baseline. Asking this question forces an explicit choice about which tail risk the model is designed to handle.
Model Properties at Glance
Six distinct interest rate model families are currently deployed in production DeFi lending. They share the same surface-level purpose: adjusting borrowing costs as a function of utilization but differ substantially in what they assume about user behavior, how they handle noise, and which failure mode they are designed to avoid. The table below gives a brief overview of each. Mathematical structure, parameter interactions, and calibration mechanics are covered in Part 2.
| Model | Reactivity | Volatility profile | Best when | Fails when |
|---|---|---|---|---|
| Linear kink | Static | Low below kink, sharp above | Utilization is predictable and stays near target | Sustained off-target conditions the model cannot correct |
| Kashi reactive | Time-scaled | Stable in range, capped extremes | Rate volatility must be bounded by design | Optimal range too narrow; noise repeatedly trips bounds |
| Euler V1 | Learns from prior response | Smoother than pure reactive | Borrower base actively arbitrages internal vs. external rates | Sudden liquidity shocks; learning lag harms response |
| Silo dynamic | Linear below critical, accelerating above | Predictable below critical, severe above | Critical utilization is the dominant risk surface | Below-critical noise dominates; linear region too quiet |
| Frax variable | Curve shifts on sustained mismatch | Stable in range, sharp at U_max | Users tolerate sharp moves to enforce range | Many interconnected parameters make calibration brittle |
| Morpho adaptive | Continuous PD-style | Volatile around target | Capital efficiency at high U_opt is the priority | Pool tolerance for IR volatility is low |
One pattern worth noting from the table: no model dominates across all four diagnostic dimensions from the previous section. Every model makes a tradeoff between rate stability and utilization control, between simplicity and adaptivity, between fast response and smooth response. The table makes those tradeoffs explicit.
Conclusion and What Is Next
This piece has focused on the qualitative diagnostic layer: what questions to ask before selecting a model, and what each model assumes. The next four parts go progressively deeper.
Part 2 covers the mathematical structure of each model - the actual equations, parameter interactions, and how small calibration choices propagate through model behavior. If you have ever wondered why a high k_p in Morpho's adaptive curve produces qualitatively different dynamics than a high γ in a linear kink, that is where we work through it.
Part 3 moves from mechanics to evidence - three months of production utilization and rate data from different lending protocols across multiple markets. The wstETH-wETH market, where the model-user mismatch produces visible IR volatility from routine utilization noise, is examined in detail.
Part 4 introduces Ipak's agent-based simulation methodology. Using a Gillespie algorithm framework for event timing and a heterogeneous-elasticity user model, we stress-test all six IR models under matched scenarios - the same liquidity shock, the same external rate shift, applied to each model so the differences are attributable to model design rather than market conditions.
Part 5 proposes the Reactive Range Model: a modification to Morpho's adaptive curve that replaces the single-point optimal utilization with a range. The modification is motivated by the volatility behavior identified in Parts 1 and 3, and Part 5 presents simulation evidence that it reduces IR volatility while preserving capital efficiency.