# A Deep Dive into the Dynamics of Interest Rate Models

**Introduction:**

In Decentralized Finance (DeFi), interest rate models (IRMs) are crucial in determining borrowing and lending dynamics within protocols. This detailed analysis explores the intricacies of IRMs in DeFi, shedding light on their fundamental principles, various types, calculation methods, and their vital role in fostering ecosystem growth and stability.

## The Essence of Interest Rate Models

IRMs are based on the interdependent relationship between liquidity availability and borrowing demand. As borrowing demand increases, depositors receive higher returns while liquidity decreases. These models are essential for managing capital flow and maintaining balance within the ecosystem.

## The Importance of Interest Rate Models

Beyond their mathematical formulations, IRMs significantly influence user behavior, capital allocation, and protocol stability. They provide a framework for predictability and transparency, fostering trust and supporting sustained growth in the DeFi space.

## Exploring the Varied Landscape of Interest Rate Models

Decentralized Finance (DeFi) boasts a diverse array of interest rate models, each tailored to specific needs and preferences within the ecosystem. Understanding the different types of interest rate models is crucial for participants seeking to engage in borrowing, lending, or liquidity provision activities. Let’s delve deeper into the various typologies of interest rate models found in DeFi:

**1. Algorithmic Interest Rate Models:**

- Algorithmic interest rate models rely on predefined mathematical algorithms to determine interest rates. These algorithms often consider factors such as market demand, asset utilization, and protocol health metrics to dynamically adjust rates.
- Examples of protocols using algorithmic interest rate models include MakerDAO’s Stability Fee algorithm, which adjusts borrowing rates for DAI based on the stability of the peg to the US dollar.

**2. Market-Based Interest Rate Models:**

- Market-based interest rate models derive rates directly from supply and demand dynamics within the market. Rates are determined by the interplay between borrowers seeking funds and lenders supplying capital.
- Protocols like Aave and Compound utilize market-based interest rate models, where rates are determined by real-time data reflecting borrowing demand and available liquidity.

**3. Pay-As-You-Earn (PAYE) Models:**

- Pay-As-You-Earn models introduce a novel approach to interest rate determination, focusing on aligning incentives between borrowers and lenders. Under this model, borrowers do not incur upfront borrowing costs. Instead, they pay fees based on the yields generated from borrowed funds.
- Stella’s PAYE model, for instance, ensures that borrowers only pay fees when they generate returns from the borrowed assets, fostering a fair and sustainable borrowing environment.

**4. Risk-Based Interest Rate Models:**

- Risk-based interest rate models assess the creditworthiness of borrowers to determine interest rates. Factors such as credit scores, collateralization ratios, and historical borrowing behavior may influence rates.
- Protocols like Cream Finance and Compound Risk Score implement risk-based interest rate models to tailor rates based on the perceived risk associated with each borrower.

Each type of interest rate model offers distinct advantages and trade-offs, catering to different user preferences and market conditions. Participants in the DeFi ecosystem can choose the model that best aligns with their risk appetite, investment strategy, and borrowing needs.

## Understanding Interest Rate Calculation

Interest rates in DeFi protocols are intricately calculated based on several key factors. These elements form the bedrock of interest rate models, influencing the dynamics of lending and borrowing transactions within the ecosystem. The primary factors include the reserve factor, borrow demand, and utilization rates. Let’s delve deeper into each of these components and their role in the calculation process.

## Key Factors in Interest Rate Calculation

**Reserve Factor:**

- The reserve factor represents a portion of the interest paid by borrowers that is set aside by the protocol. This reserve can be used for various purposes such as covering potential losses, contributing to the protocol’s treasury, or funding further development.
- The reserve factor effectively creates a spread between the borrow rate and the supply rate, ensuring the protocol retains a portion of the interest for sustainability and operational purposes.

**2. Borrow Demand:**

- Borrow demand is the total amount of assets that users want to borrow from the protocol. High borrow demand typically leads to increased borrowing interest rates as the protocol seeks to balance the supply and demand of assets.
- When borrow demand is high, it signals strong user interest in borrowing, prompting the protocol to increase interest rates to manage liquidity and prevent the depletion of available funds.

**3. Utilization Rates:**

- Utilization rate is a critical metric in DeFi interest rate models. It is calculated as the ratio of borrowed funds to the total available supply of funds in the protocol.
- The utilization rate provides insights into how much of the available liquidity is being used for borrowing. It directly impacts the interest rates for both borrowers and lenders.

## Utilization Formula

Utilization is typically calculated as follows:

Utilization = Borrow Demand/ Total Deposits

- If total deposits increase while borrow demand remains unchanged, utilization decreases. Conversely, if borrow demand increases relative to total deposits, utilization increases.

## How Utilization Drives Borrow Interest Rates

Utilization plays a pivotal role in determining borrowing interest rates. In a well-designed protocol, changes in utilization lead to corresponding adjustments in interest rates to maintain equilibrium. Here’s how utilization influences borrowing interest rates:

**When utilization rises (indicating high borrowing demand):**- Borrow and supply interest rates increase.
- Lending is incentivized as higher interest rates attract more depositors.
- Borrowing is disincentivized due to higher costs.
- As a consequence, idle liquidity increases, and borrow demand falls, leading to a lower level of utilization.
**When utilization falls (indicating excess idle liquidity):**- Borrow and supply interest rates decrease.
- Borrowing is incentivized due to lower costs.
- Lending is disincentivized as lower interest rates reduce depositor attraction.
- As a consequence, idle liquidity decreases, and borrow demand rises, leading to a higher level of utilization.

The function that translates the utilization level to the borrow interest rate is defined by the interest rate model, with parameters usually set by protocol governance to achieve desired economic outcomes.

## Relationship Between Borrow Interest Rate and Supply Interest Rate

The relationship between borrow interest rates and supply interest rates is typically determined by the protocol’s interest rate model. Here’s a simplified overview of how this relationship is structured:

- Borrow interest rate is usually higher than the supply interest rate to ensure the protocol can cover its obligations and maintain reserves.
- Not all lending protocols set the supply interest rate using the same formula. For example, Compound V3 calculates the supply interest rate directly based on utilization and does not factor in the borrow rate.

**Worked Example:** Consider a scenario where the borrow rate is 10%, the utilization level is 50%, and the reserve factor is 20%. The interest rate for depositors (supply rate) would be calculated as follows:

Supply Rate=Borrow Rate×Utilization Level×(1−Reserve Factor)

Supply Rate=10%×50%×(1−20%)=5%×80%=4%

This example illustrates that a portion of the borrowed interest is retained by the protocol (the reserve factor), and depositors earn interest based on the remaining amount.

## Optimal Utilization and Protocol Stability

DeFi protocols aim to achieve an optimal utilization rate, typically between 80–95%. This range is considered ideal because:

- It ensures there is sufficient liquidity available for withdrawals, preventing a situation where all funds are lent out and lenders cannot access their deposits.
- It balances the incentives for both borrowers and lenders, maintaining a healthy demand for borrowing while ensuring attractive returns for depositors.

To achieve optimal utilization, interest rate models often incorporate piecewise linear and “kinked” supply curves. These curves rise slowly up to the optimal utilization point and then increase more sharply, creating strong incentives for behavior that maintains the desired balance within the protocol.

## The Kick Parameter in Interest Rate Models

The Kick parameter is an innovative concept used in certain DeFi protocols to dynamically adjust borrowing interest rates based on the utilization rate. This mechanism is designed to maintain equilibrium within the protocol by incentivizing appropriate borrower and lender behaviors as market conditions change. Here’s a detailed breakdown of how the Kick parameter works and its significance:

## Understanding the Kick Parameter

The Kick parameter represents a threshold utilization rate at which the borrowing interest rate formula changes significantly. When the utilization rate reaches this threshold (known as the Kick point), the borrowing interest rate increases more sharply compared to the rate of increase at lower utilization levels. This abrupt change, often referred to as a “jump rate model,” helps in managing liquidity and ensuring the stability of the protocol.

## Borrowing Interest Rate Model with the Kick Parameter

The borrowing interest rate model can be divided into two distinct phases: before and after the Kick point.

**Before the Kick Point:**At lower utilization rates, the borrowing rate is calculated using a formula that gradually increases with the utilization rate. This can be expressed as:

Borrowing Rate=rf+2×Utilization Rate×rf

- Where:
**rf**is the risk-free rate, representing the return that the DeFi protocol can secure from quasi-risk-free sources.

**After the Kick Point:**Once the utilization rate reaches the Kick point, the borrowing rate formula changes to reflect a steeper increase. This new formula is designed to rapidly adjust the borrowing costs, thereby incentivizing lenders to supply more funds and borrowers to repay their loans.

The post-Kick formula is:

where:

**Kick**is the utilization rate at which the borrowing rate formula changes. Typically, this point is set at 80%.**rKick**is the borrowing interest rate at the Kick point.**max**is the maximum borrowing interest rate, reached when the utilization rate is at 100%.

## Significance of the Kick Parameter

**Incentive Alignment:**The Kick parameter helps align incentives between borrowers and lenders. By increasing borrowing costs significantly at higher utilization rates, it encourages borrowers to repay loans when liquidity is low and rewards lenders with higher returns when they provide additional capital.**Liquidity Management:**The sharp increase in borrowing rates beyond the Kick point acts as a mechanism to prevent the depletion of liquidity within the protocol. It ensures that there is always enough liquidity available for withdrawals, thereby maintaining the stability and functionality of the protocol.**Market Responsiveness:**The dynamic nature of the Kick parameter allows the interest rate model to be more responsive to market conditions. As utilization rates fluctuate, the borrowing rates adjust in real-time to reflect these changes, helping to maintain an optimal balance between supply and demand for funds.**Mitigating Risks:**By discouraging excessive borrowing at high utilization rates, the Kick parameter helps mitigate the risk of liquidity crises. This is crucial for the long-term health and sustainability of the DeFi protocol, as it prevents scenarios where all funds are lent out, and lenders are unable to access their deposits.

## Example: Borrowing Rate Graph of CAKE Token

To illustrate the effect of the Kick parameter, consider the borrowing rate graph for the CAKE token in a DeFi protocol using this model. The graph shows a gradual increase in the borrowing rate up to the 80% utilization rate (Kick point). Beyond this point, the rate increases more steeply, reflecting the jump rate model.

## Parameters:

**rf (Risk-Free Rate):**The baseline rate obtained from quasi-risk-free sources.**rKick (Rate at Kick):**The borrowing interest rate at the 80% utilization threshold.**max:**The maximum borrowing interest rate at 100% utilization.

*Each asset has different rf, rKick and max parameter.*

By examining such a graph, participants can understand how borrowing costs will change as utilization rates approach and exceed the Kick point. This transparency helps users make informed decisions about borrowing and lending activities.

The return to Lenders is determined as:

Lending Interest Rate=Borrowing Interest Rate∗UtilisationRate

In summary, the Kick parameter is a crucial component of advanced interest rate models in DeFi, providing a mechanism to dynamically adjust borrowing costs based on liquidity conditions. Its implementation helps maintain protocol stability, align incentives, and ensure a resilient DeFi ecosystem.

## Issues with Traditional Interest Rate Models (IRM)

Traditional interest rate models (IRMs) in Decentralized Finance (DeFi) face several challenges that can impact the efficiency, fairness, and stability of the ecosystem. Understanding these issues is crucial for stakeholders seeking to address and mitigate potential drawbacks. Let’s delve into some of the key issues with traditional IRMs:

**1. Misaligned Incentives:**

- Traditional IRMs often create a zero-sum game between lenders and borrowers, where one party’s gain comes at the expense of the other. Borrowers may face high interest rates, putting pressure on them to generate even higher yields to cover borrowing costs. This dynamic can lead to an unsustainable environment where borrowers are incentivized to take excessive risks to achieve profitability, potentially compromising the stability of the protocol.

**2. Disconnection from Market Yields:**

- Traditional IRMs may not accurately reflect the actual yields available in the broader market. This disconnect can result in inefficiencies and reduced incentives for borrowers to participate in DeFi protocols. If borrowers can achieve higher yields elsewhere in the market, they may be less inclined to borrow from DeFi platforms, leading to decreased borrowing demand and liquidity within the protocol.

**3. Impact of Large Players:**

- The presence of large players, such as whales and institutions, can significantly impact interest rates in traditional IRMs. When these entities engage in large borrowing or lending activities, they can quickly deplete available liquidity or create spikes in demand, leading to increased interest rates. This situation can disadvantage smaller borrowers and lenders, who may face higher costs or reduced yields due to the actions of larger players. Additionally, high utilization driven by large players can result in negative annual percentage yields (APY) for smaller participants, further exacerbating disparities within the ecosystem.

## 4. Lack of Flexibility and Adaptability:

- Traditional IRMs may lack the flexibility to adapt to rapidly changing market conditions. As DeFi continues to evolve and new challenges emerge, IRMs must be able to adjust dynamically to maintain protocol stability and competitiveness. Rigid or outdated models may struggle to cope with shifting demand patterns, leading to suboptimal outcomes for participants.

Addressing these issues requires innovative approaches and the adoption of alternative interest rate models that better align incentives, accurately reflect market yields, and promote fairness and stability within the DeFi ecosystem. By recognizing and mitigating the shortcomings of traditional IRMs, stakeholders can foster a more resilient and inclusive financial infrastructure in DeFi.

**Benefits of the Pay-As-You-Earn Model**

**Fair and Genuine DeFi Yields:** By aligning the incentives of borrowers and lenders, the PAYE model facilitates a more equitable distribution of yields. This could lead to more sustainable and genuine DeFi opportunities.

**Innovation in Leveraging and Lending:** The introduction of the PAYE model represents a fundamental shift in how leveraging and lending can be approached in DeFi, potentially setting a new standard for the industry.

Pay-As-You-Earn model addresses the shortcomings of the traditional IRM by eliminating borrowing costs, aligning incentives between borrowers and lenders, and distributing yields more equitably. This approach enhances capital efficiency and paves the way for more sustainable and genuine yield generation in the DeFi space.

## Conclusion

Interest rate models (IRMs) are the foundation of DeFi, crucially influencing borrowing and lending activities. While traditional IRMs have driven DeFi’s growth, they face challenges like misaligned incentives, market disconnects, and the influence of large players. These issues necessitate the adoption of innovative models such as the Pay-As-You-Earn (PAYE) model, which aligns borrower and lender interests more effectively.

A thorough understanding of IRMs is essential for navigating the DeFi landscape. By addressing the limitations of traditional models and embracing more adaptive approaches, the DeFi ecosystem can achieve greater stability, fairness, and sustainable growth. As DeFi evolves, continuous refinement of IRMs will be key to unlocking its full potential and ensuring a resilient financial future.