dCDS

We discuss about the dCDS concept and the user flow for participating in dCDS module.

Decentralised Credit default swaps (dCDS) is the derivative instrument which allow users to swap a percentage of the credit risk of the borrowers and also provide a volatility hedge to borrowers in return for fixed fees being shared from multiple borrowers thus diversifying the risk over multiple borrowers. Users can enter into a dCDS module by depositing USDA+, USDT or any other volatile token's acceptable by the protocol.

By credit risk, we mean the probability of a borrower defaulting on their stablecoin loans even after getting protection against collateral volatility.

The protocol covers the volatility risk or provides downside protection by utilising the funds with reserves in dCDS. The funds are used to swap the credit & volatility risk which might emerge from user defaulting on their loans or collateral volatility. Every user position in dCDS is treated like a virtual put option seller. So, the dCDS users are essentially long on ETH/tokenised ETH assets. In return for acting as a virtual put option seller, they receive the option fees from multiple borrowers. They are also receive around 3% - 5% of the ETH collateral upside when a borrower closes their positions and repays the stablecoin loan. The yield per dCDS user can reach as high as 200% as per conservative estimates in our simulation model

The dCDS module plays multiple roles as mentioned below

dCDS and See-Saw function mechanism

As an Option Seller

Users can deposit USDA+, USDT or any other acceptable token in the dCDS module. The module will calculate the proportion of amount deposited from the total deposited value from a combination of all deposits and accrue the fixed fees from borrowers to dCDS users.

Providing Instant re-deemability of USDA+

Users looking for re-deemability of USDA+ so as to convert their assets to cash within the protocol itself. Here, users can deposit USDA+ in our dCDS module and get USDT from the reserve which can be easily converted into cash. The USDA+ deposited will be utilised to offer volatility hedging.

Fees accrual mechanism

The total amount to be returned to the dCDS holder after a particular time period includes the summation of the option fees accrued through various borrowers, volatility hedging gains and liquidation gains.

Accrual of Volatility gains

The exchange of funds between the ETH vault and the dCDS pool will be calculated after intiation of a dCDS withdrawal or closing of position by borrower. As soon as a dCDS deposits funds into our platform, we will identify the below values.

1. Current ETH market price, Er

2. Ratio of dCDS deposit/Total dCDS deposited funds till now (Ci/C)

3. Total number of ETH holdings in our ETH pool

We will then calculate the current value of dCDS holder in our protocol

Total dCDS Deposited Funds = C

dCDS user deposited amount = Ci

dCDS user current value = Cr1 = Cd + (Ci/C)*(Er - Ei)*(Total Collateral Holdings)

We will calculate the division of exchanged funds among the total dCDS depositors. As soon as there is a new depositor or borrower or any sort of new event, the value of different figures in the above formula will change. After the new event, the division percentage of exchanged funds will be changed accordingly.

Thus, new Cr2 = Cd + (Cd/C)*(Er- Ei+1) * (Total ETH Holdings) Final dCDS user value during withdrawal

$$Cr = Cd+\sum \limits_i^j (Ci/C)*(Er-Ei)*(Total Collateral Holdings)$$

So, after every event, the reward percentage split changes, which mandates the protocol to calculate the rewards split between two deposit intervals among all the dCDS depositors until that moment. This exercise will be too computationally intensive for the smart contract considering there might be 100s of thousands of dCDS depositors. Also, calculating the reward split before every new dCDS deposit would delay the transaction completion time and considerably affect the user experience.

In order to manage the above situation, we will maintain a record of reward split for only one standardized deposit amount. For the start, we have considered that deposit amount to be 1000 USDA+. So, before every new dCDS deposit transaction, we will calculate the proportionate reward for 1000 USDA+ worth of deposits and update the total amount after every transaction. By recalculating the division percentage of exchanged funds, we will be able to determine the final amount to be returned to the dCDS when they try to close their position. The total amount for a particular dCDS will be a fraction or multiple of the current total amount of the standard 1000 USDA+ deposit figure. This allows us to identify the value accrued to a dCDS position during the time of withdrawal, which is one of the critical values to calculate in the operation of our Delta Neutral (See-Saw) contract.

Above is a mechanism to calculate the volatility related gains/losses as per the collateral price changes for the locked time duration.

Accrual of Option Fees gains

To calculate the option fees accrued to dCDS users, we calculate the normalized amount of dCDS holders and capture the cumulative rate of option fees % change. The continuous accrual of option fees to dCDS holders is initiated by multiplying the normalized amount by the option fees cumulative rate. The resulting amount is the summation of fees accrued from all borrowers. To maintain a ratio of >=0.2 for dCDS Vault/ETH Vault, the yield accrued per dCDS participant is a summation of fees from at least 5 borrowers. Users locking funds for longer durations can accrue 200%+ yields without any loss of capital

Calculation of Option Fees

1. Whenever a user opens a position in the borrowing module then we will calculate the option fees for the user by initiating a API call from backend to capture volatility and calculate the per ETH option fees.

2. The option fees will be then calculated for the user as per the total ETH and strike price selected by the user.

3. This option fees will be deducted from the minted/loaned USDA+ amount from user position and added in treasury.

4. The same amount will be stored in the backend for the particular user.

5. Timestamp of 30 days will be added against every user in the backend for 30 days option maturity

We will be utilising a combination of approaches for calculating Option fees. Each of these approaches involve calculation of collateral volatility or standard deviation. So, below series of steps are performed for update of collateral volatility values

1. Collect Data: Gather historical price data for collateral over the chosen timeframe (daily, hourly, etc.).

2. Calculate Returns: Compute the daily returns by taking the natural logarithm of the ratio of today's closing price to yesterday's closing price: i.e log ( n/n-1)

3. Calculate Average Return: Find the average return (mean) of the series calculated in step 2.

4. Calculate Variance: Compute the variance by squaring the differences between each return and the average return, then averaging those squared differences.

5. Calculate Standard Deviation: Take the square root of the variance to get the standard deviation, which represents the volatility.

$$Standard Deviation = \surd \bigg(\sum \limits_i^n (Ri - AverageReturn)^2/ (n-1)\bigg)$$

Assuming, ETH as collateral ETH Volatility = a dCDS Vault value/ ETH Vault value (including borrower’s ETH value) = b Current ETH price = Er

Minimum Option Price always >= 20 USDA+ for $1000 worth of ETH value

Option Price per 1 ETH = (10*a*Er)^½ + 3*(1/b) The full explanation and calculation will be mentioned in the whitepaper to be released.

Accrual of Liquidation Gains

Liquidation gains occur when any borrower touches the LTV of 100% and hasn't paid his loan yet. As the borrower has now went into liquidation stage so any kind of downside protection accounted for the user is no longer required. The dCDS users who have opted for liquidation gains will be getting the below values Liquidation Gain = Total Collateral of borrower + 20% Downside protected amount

The thing to note here is that the liquidation gain is now only split among users who have opted for liquidation gains. But the 20% downside protection given to user is provided by every dCDS user. Assuming dCDS User Ci has opted for Liquidation Gain Also, assuming only 25% of the dCDS users have opted for Liquidation gains dCDS module will be creating a Liquidation index where every dCDS user will be tagged to the Liquidation index when the initial deposit was made. For Ci, Let's say Li is the Liquidation index at deposit and Lj is the Liquidation index during withdrawal of Liquidation gains by Ci Total dCDS pool funds = C Dx & Ex are the collateral amount and ETH price of borrower during Liquidation

Liquidation Gain for Ci can be calculated as summation of Li through Lj

$$C(x) = \sum \limits_i^j Dx *Ex * (Ci/C)$$

The protocol initiates the transfer of Liquidated collateral amount among all the dCDS users who have opted for liquidation and the resulting Liquidation gain over a series of these liquidations for every user can be calculated through above formula.