Product Update Issue 2: By the Numbers — Economic Advantages of C-OP

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UNN Finance Updates & Ideas

8 min readJan 18, 2021

In our inaugural issue of Product Update, we outlined our Collateral Optimization (C-OP) product — an American-style put option instrument using the Binomial Model to enhance capital efficiency of borrowers on lending protocols. We detailed the market fit for C-OP, expressed why we selected our modelling choices and projected the benefits of C-OP for improving capital efficiency while retaining a similar risk profile for lending platforms.

In this issue, we illustrate the explanations with a sample case study and tangible numbers.

This exercise proves that in addition to freeing collateral for users, C-OP has non-linear cost savings to liquidations: the bigger the gap down in asset price, the more the C-OP saves the borrower.

Capital Efficiency beyond Lower Collateral Requirements

One of the easier to grasp benefits for C-OP is the net positive impact on capital efficiency in DeFi. By reducing high over-collateralization (OC) ratios for crypto asset collateral, such as from 150% to 125%, we unlock more fluid composability, risk management, and improved capital deployment.

However, C-OP goes beyond advancing capital efficiency primitives with lower collateral requirements alone. There are more powerful advantages that include:

Augmenting the borrowing capacity during positive price movements.
Increasing account resilience to liquidations.
Non-linear reduction of opportunity and the actual cost of liquidation.

Before proceeding with our example, we define two parameters that protect the overall risk to the lending platform and responsibly constrain the amount of C-OP a user can activate: Maximum Protection Composition (MPC) and Capacity to Free Post Liquidation (CFPL).

MPC and CFPL Risk Parameters

The MPC is the maximum borrowing capacity for collateral that can be freed up from the amount the user is borrowing using C-OP. In TradFi terms, we limit the composition of derivatives qualified for margins in a portfolio. For every $1 of borrowing capacity used, MPC allows a maximum % of that $1 to be optimized with C-OP. If MPC is set at 25%, then for every $1 of borrowing capacity, $0.25 can be optimized with C-OP. With Alice’s deposit of 10 ETH at $10,000 and an MPC value of 25%, the max C-OP amount for Alice’s collateral is $1,250 (2.5 ETH = ¼ of 10 ETH).

MPC is collateral-specific, given that movements in different asset prices are distinctive, and C-OPs in one asset may not trigger while another asset drops, which triggers account liquidation.

The CFPL is the threshold of excess capacity that a lending liquidator needs to free for an account with negative borrowing capacity. For example, assume Alice is using 100% of her borrowing capacity; that is, all $5,000 in borrowing capacity from Alice’s ETH was used to borrow DAI. In addition, assume the CFPL for liquidators is set at 25%. Should Alice’s ETH value fall, which means Alice has negative account liquidity, liquidators will auction off her ETH collateral until the CFPL is above 25% of her total borrowing capacity at the time of liquidation.

Both MPC and CFPL can be configured to the lending protocol’s risk tolerance and adjusted in the face of changing market conditions. For the purposes of our example, we define both MPC and CFPL as 25%.

C-OP Economics by Example

Let’s consider the case of Alice, who deposits 10 ETH into Compound to borrow DAI with ETH at the price of $1,000 at the time of her borrow. Every deposited asset has a borrow factor, which determines the borrowing capacity that the asset can contribute. With a borrow factor of 0.5 for ETH, Alice can borrow $0.5x worth of assets (in this case, DAI) per 1 ETH deposited. So, Alice’s initial deposit of 10 ETH is worth $10,000 and allows her to borrow $5,000 of assets while retaining her 10 ETH exposure.

With the details above, we run through 3 outcomes and make a side-by-side comparison of Alice not using C-OP and Alice protecting herself with C-OP. The 3 outcomes are:

The price of ETH (currently $1,000) gaps up to $1,500.
The price of ETH (currently $1,000) gaps down to $950.
The price of ETH (currently $1,000) gaps down to $749.998.

Pricing C-OP

To determine the amount of C-OP Alice will purchase, we convert the $ value into ETH equivalent. In essence, C-OP is an option contract where contract size = 1. That is, 1 C-OP bought = 1 asset (ETH). Thus, given MPC of 25% on 10 ETH at $1,000 per ETH, assuming she purchases the maximum amount of C-OP allowable, Alice will buy $1,250 (ETH) worth of collateral. The $1,250 translates to 2.5 C-OP contracts ($1,250 divided by ETH price divided by the borrow factor of ETH).

To price the C-OP, use the following options parameters:

Amount C-OP selected by Alice = 2.5 ETH
Term Length = 30 days
Annual Realized Volatility = 160%
Strike = $1,0002
Cost of C-OP = $448 (for 2.5 contracts)
Borrow Capacity Freed = 25%

Outcome One — Price of ETH Gaps up to $1,500

No C-OP

If the price of ETH surges to $1,500 during her open position on Compound, Alice’s 10 ETH is now worth $15,000 alongside her $5,000 of DAI, with no fear of liquidation. Alice’s borrowing capacity has increased by $5,000, meaning she now has an additional borrow factor of $2,500 in DAI.

Now, Alice’s borrow capacity, rather than being 100%, is 67% as the ratio of her ETH value relative to the size of the loan has decreased. Alice is not at risk of liquidation.

Optimized with C-OP

With C-OP, in addition to the $2,500 increase in ETH with C-OP, Alice has an additional $1,250 free borrowing capacity due to C-OP. In other words, Alice has a total of $3,750 in extra borrowing capacity. Additionally, Alice’s borrowing capacity is only at 50%, rather than 67% without C-OP.

Alice now has a sizable advantage in capital efficiency using C-OP during positive price momentum with her open position on Compound.

Outcome Two — Price of ETH Gaps down to $950

No C-OP

With the price of ETH gapping down to $950, Alice’s account liquidity becomes negative since the borrowing value of her ETH holdings has decreased to $4,750. With Alice’s borrowed amount of $5,000 in DAI, her current borrowing capacity is 105% with account liquidity at -$125.

A liquidator will step in to liquidate the account back to the 25% CFPL.

The total collateral needed to free up and restitute Alice’s position is $1,437.50 since the amount to be liquidated to restore the CFPL is $1,187.5 (25% of the borrowing capacity of $4,750 = $1,187.5) ) plus the -$250 of current negative liquidity.

As a result, the amount of Alice’s ETH collateral sold off at a current price of $950/ETH is 1.51 ETH.

Optimized with C-OP

In this scenario, we can highlight C-OP’s power to protect Alice’s collateral in volatile, downward market conditions.

When the ETH price gaps down to $950, Alice’s account liquidity decreases by the same amount as no optimization (-$250). However, because there is excess collateral of $1,250, Alice still has an excess capacity of $1,000. With a borrowing capacity of 79 percent and positive account liquidity, Alice is not liquidated.

This is worth repeating: liquidation does not even trigger for Alice’s position.

Overall, Alice’s liquidation savings are 321%, using a simple calculation of the value of ETH sold in case of liquidation when not optimized divided by the cost of buying C-OP. We don’t even factor in the opportunity cost of losing the 1.51 ETH or the liquidation fees that range between 5–15%.

Interested? It gets better.

Outcome Three — Price of ETH Gaps down to $749.998

No C-OP

In this scenario, the ETH price declines further, hitting $749.998. Alice’s account liquidity is now even more in the red, at -$1,250 relative to the borrowed amount of $5,000 in DAI and borrowing capacity is now 133%.

The liquidator brings the account back to CFPL by liquidating $937.495 of ETH ($750 * 10 ETH * 0.5 Borrow Factor * 25% CFPL = 937.4975) on top of the negative $1,250 in negative liquidity for a total of $2,187.51 worth of ETH.

The liquidator has now sold off 2.92 of Alice’s ETH collateral to restore her account to good standing.

Optimized with C-OP

Alice’s account liquidity is also negative, but only at -$0.01, with basically 100% usage of her borrowing capacity. Her position enters liquidation, and the collateral to be liquidated to reach parity with the CFPL is $937.51 (same as the no C-OP case) plus only the negative $0.01. Furthermore, C-OP is exercised by the lending protocol equating to the recovering amount = (strike — current price) * number of contracts bought = ($1,000 — $749.998) * 2.5 = $625.

After subtracting the C-OP covered amount, the remaining balance of collateral to free up is covered by selling ETH, for a total of 0.41667 ETH sold. This is compared to the no C-OP amount of 2.92 ETH sold.

Alice’s liquidation savings of 288% are a vast improvement over sharp downward price swing cases without C-OP.

Summary

As always, a picture (or two) is worth a thousand words. We first graph Alice’s borrowing capacity with and without C-OP against the price of ETH. Alice’s much higher tolerance for liquidation can easily be seen in the lower ETH price intercept of ~$750.

C-OP provides more borrowing power and lower liquidation triggers — a beneficial outcome for risk-taker who want to borrow more, or for conservative borrowers who want more protection.

Next we plot the amount of ETH liquidated relative to the ETH spot price with and without C-OP.

The opportunity cost of lost collateral is an easily missed, but even more critical benefit of avoiding liquidations with C-OP.

Now, we can truly appreciate the downside protection that C-OP enabled for Alice. The number of ETH liquidated with C-OP is markedly less than without C-OP. Even in cases where lending protocols put in place lower CFPL, C-OP protection remains substantial.

In conclusion, C-OP not only improves Alice’s borrow capacity in both positive and negative price movements of her underlying collateral, C-OP mitigates downside liquidation risk for Alice. In fact, the larger the price decline in Alice’s collateral ETH, the more C-OP saves of Alice’s collateral. C-OP even mitigates the risk of liquidation in smaller price downswings, making collateral deposits on lending protocols more robust to marginally volatile market conditions.

Capital efficiency is enhanced on both ends — greatly mitigating the downside risk and augmenting the borrowing capacity during bullish price swings. Win-win.

Notes

For purposes of clarity, we exclude the cost of gas, slippage, etc.
The strike of option is set at the same time the borrow is made, ensuring that the optimized borrowing capacity calculated for the user on the underlying collateral is properly recreated with the option. In this case, the spot price is $1,000.