Arcadia Collateral Risk Simulation: Progress Report 4

From LlamaRisk

In our  previous progress report , we reviewed the simulation and validation processes to showcase how we ensure the simulation functions as intended. This week's report will dive deeper into the empirical borrower model and what the implications are on realism for the model.

This progress report is structured into four parts:

Empirical Borrower Distribution

The empirical borrower distribution provides an idea of borrower behavior in digital asset lending markets. This analysis shapes our simulation models by informing key assumptions and parameters when initializing the borrower model and creating a more realistic simulation. Through this, we gain essential insights into how a potential borrower can look in Arcadia.

Method 1: Total borrow vs Collateralization Ratio (CR) based on collateral vs numeraire token pairs.

Method 1 entails a comparative analysis of total borrow amounts versus collateralization ratios (CR) for assets akin to collateral and numeraire token pairs at launch. It quantifies borrowing patterns by plotting loan amounts against CRs. It offers insight into lending behaviors of the reference protocol and acts as a proxy for Arcadia's future user base.

The chart above quantitatively analyzes the relationship between collateralization ratios and the log-transformed borrowing amounts in USD. The x-axis represents the Collateralization Ratio, a measure of the value of collateral provided for loans. The y-axis shows the borrowing amount on a logarithmic scale, enabling an adequate representation of a wide range of values.

Data points are dispersed across the chart, with contour lines indicating the density of these points. The concentration of data points within certain regions suggests common borrower behaviors and collateralization practices.

Marginal distributions on the top and right axes show the Kernel Density Chart of the Collateralization Ratios and borrowing amounts, respectively, offering a clearer view of their distributions.

Method 2: Empirical Distributions of Collateral for a given Borrow Position

For the second method, we apply a filter to identify borrow positions that involve a specific numeraire collateral asset pair, anticipated with the launch of Arcadia. Considering our reference protocol is a lending platform, borrowers may have several borrow positions against various types of collateral. This contrasts with an Arcadia Margin account, which permits borrowing of only one asset against a collateral set for any given Margin Account. To reconcile these differences, we adjust the size of each borrowed asset relative to the total borrowing and proportionately modify the collateral distribution to reflect this specific asset.

The chart above shows a heatmap visualizing the distribution of collateral types across different bins of borrow amounts (for a reference lending protocol) for USDC/USDCB. The x-axis represents the bins of borrow amounts, categorized by their log10 values ranging from 1 to 7. The y-axis lists various collateral assets. Each cell within the heatmap provides a proportional value, represented by both color intensity and a numeric label, indicating the share of a particular collateral type used for the corresponding borrow amount bin.

Key observations include:

This heatmap examines the patterns and preferences related to collateral among borrowers across various borrowing tiers within the lending platform. It provides insights into the potential distribution of borrowings for specific types of collateral. To initialize the borrower model, we have two approaches: we can predict the likely collateral distribution based on the size of the collateral sample, or we can directly draw samples from empirically observed borrower positions. Incorporating this element adds a layer of realistic borrower behavior to our simulation, thereby increasing its authenticity.

Goals for Week 8

For Week 8, the team is focused on the following objectives to develop further and refine our simulation model:

Progress Report:

As we conclude Week 7, our team has made substantial progress in advancing the simulation model, with a few objectives still being fully realized. Here is an overview of our achievements and ongoing efforts: