Example

Case 1: User in a healthy position

Following the post on Delta and the liquidation logic, we think a full example of liquidation calculations is useful. Suppose that the initial conditions of the position taken by the user are:

Ratio Finance Risk Tolerance	Market Conditions	Borrower's position
$\Delta_{min}$ = 2%	Market Price = $1.02	LP Tokens = 1000
Tolerance = 1.25	Fair Price = $0.98	Debt Taken = 100%
Collateralization Ratio = 130%
$\Gamma$ = 0.2%

Following the calculations before we have the following conditions for liquidation

Borrower's Position	Risk monitoring
Maximum Borrowable USDr = $784.62	Delta = 4.66%
USDr Debt = $784.62	Dynamic CR = 128.15%
Collateral to Debt = 130%	$\Gamma$ = 0.2%
	Health = 1.85%
	Liquidate Flag = FALSE

In this case nothing needs to be done, the user is in a healthy position and there isn't any liquidation.

Case 2: User repays to be safe

Here we start from the same initial conditions as the example above, however different market conditions pushed LP Market price to $1.01 and Fair Price to $0.85.

Ratio Finance Risk Tolerance	Market Conditions	Borrower's position
$\Delta_{min}$ = 2%	Market Price = $1.01	LP Tokens = 1000
Tolerance = 1.15	Fair Price = $0.85	Debt Taken = 100%
Collateralization Ratio = 130%
$\Gamma$ = 0.2%

The current market conditions are such that:

Borrower's Position	Risk monitoring
Maximum Borrowable USDr = $ 776.92	Delta = -1.15%
USDr Debt = $ 784.62	Dynamic CR = 131.15%
Collateral to Debt = 128.73%	$\Gamma$ = 0.2%
	Health = -2.42%
	Liquidate Flag = TRUE

Then the amount to repay to be safe can be easily calculated:

Repay (%)	LP Tokens to deposit	USDr to repay
CR - CTD = 1.27%	Repay (%) * 1000 = 12.75	12.75 * $ 1.01 = $ 12.87

At the end of this repayment process the borrower goes back to a healthier position where:

New CTD	New Health
131.23 %	0.08%

Case 3: User getting partially liquidated

Here the same conditions as the example above are given, but the borrower didn't repay any of their debt within the 3 epochs of time given as a buffer before liquidation occurs.

Ratio Finance Risk Tolerance	Market Conditions	Borrower's position
$\Delta_{min}$ = 2%	Market Price = $1.01	LP Tokens = 1000
Tolerance = 1.15	Fair Price = $0.85	Debt Taken = 100%
Collateralization Ratio = 130%

In this case the ratio between Market Price and Fair Price has dropped considerably and the position of the user needs to be liquidated

Borrower's Position	Risk monitoring
Maximum Borrowable USDr = $ 776.92	Delta = -1.15%
USDr Debt = $ 784.62	Dynamic CR = 131.15%
Collateral to Debt = 128.73%	Health = -2.42%
	Liquidate Flag = TRUE

In this example, at current market conditions the borrower's debt is now under-collateralized, therefore, the position needs to be readjusted. For this particular example this readjustment is:

Liquidation results	User perspective
Minimum Liquidation = 25%	New LP Position = 750
Tokens to be unwound = 250	New LP Nominal = $ 757.50
LP Notional Value = $ 252.66	New USDr Debt = $ 531.95
USDr Burnt = $ 194.35	New Collateral to Debt = 142.40%
	New Health = 11.25%

A full calculation of this example can be found in the following link https://docs.google.com/spreadsheets/d/1OIbpjnNHeSDOufd7lC7i6tk8aRZ1VLSEgX4N9yQN5Vc/edit?usp=share_link