Margin Calculations

The Margin of an Arcadia Account can roughly be seen as the value of collateral assets that a Debtor must hold in a Margin Account to cover the credit risk of its Creditor(s). It is the value of assets that is "locked" when a Debtor opens a position.

Margin Requirements

There are three different account states, as shown in the following figure, depending on the Used Margin of the Account and the risk-adjusted total values of the Account.

Margin Account health states

1. Healthy state:

The Account is in a healthy state if the used margin is smaller than the Collateral Value:

$$um < v_{coll}$$

No account actions are restricted for Accounts in a healthy state, as long as the Account is still healthy at the end of the action.

2. Unhealthy state:

The Account is in an unhealthy state if the used margin is smaller than the Collateral Value but bigger than the Liquidation Value:

$$v_{coll} < um < v_{liq}$$

Accounts in the unhealthy state can only be de-risked by reducing the open position or adding more collateral assets. It is not possible to withdraw any asset or to increase the open position.

3. Liquidatable state:

The Account is in a liquidatable state if the used margin is larger than the Liquidation Value:

$$v_{liq} < um$$

When an account is in the liquidatable state, anyone can trigger a margin call. The Account is now frozen, and the liquidation process of the Account starts. The liquidation ends when either the Account is brought back to a healthy state, or all assets are liquidated.

Margin Calculations

Collateral Value

The Collateral value is the sum of the MtM (mark-to-market) value, discounted with the risk factor (the Collateral Factor) of each asset in the account.

$$v_{coll}^{c} := \sum_{i} CF_{i}^{c} \cdot v_{i}(a_{i})$$

The Collateral Factor is equivalent to the Initial Margin as is commonly used in traditional finance.

$$CF_{i}^{c} = \frac{1}{1 + IM_{i}^{c}}$$

Liquidation Value

The Liquidation value is the sum of the MtM (mark-to-market) value, discounted with the risk factor (the Liquidation Factor) of each asset in the account.

$$v_{liq}^{c} := \sum_{i} LF_{i}^{c} \cdot v_{i}(a_{i})$$

The Liquidation Factor is equivalent to the Maintenance Margin as is commonly used in traditional finance.

$$LF_{i}^{c} = \frac{1}{1 + MM_{i}^{c}}$$

Available Margin

We define the available margin, $am$, as the total value that the Account can use as margin to secure liabilities.

Hence the Available Margin is nothing different then the previously defined Collateral Value:

$$am = v_{coll}^{c}$$

Open Position

The open position, $op^c$, equals the size of the liability that a specific Debtor has with a specific Creditor.

Minimum Margin

As explained in Liquidations, the minimum margin, $M_{min}^c$, is the minimum amount of Collateral Value that must be held in an Account to be able to open a position with a Creditor.

Used Margin

The used margin, $um$, is the total amount of Collateral Value locked by the Account to ensure that the Account remains over-collateralized.

Since collateral in the Account must be held to cover both the open position and the minimum margin, the used margin can be found as:

$$um := M_{min}^c + op^c$$

Free Margin

The free margin, $fm$, is the remaining amount of Collateral Value that can be used to increase the open position or that can be withdrawn from the Account's assets.

The free margin can be found by subtracting the used margin from the available margin:

$$fm := am - um$$

Examples

Coming soon.