Collateral algorithms

A collateral algorithm computes, for each netting set, time point, and scenario, the collateral balance that the CSA requires. The collateralized exposure measures subtract this balance from the netted mark-to-future (MtF) value. Netting Set Analytics provides two algorithms: Bilateral CSA and Unilateral (Bank) CSA. A cube builds one folder of collateral measures per algorithm that it wires, named Collateralized Exposures - <algorithm name>. The PFE cube wires Bilateral CSA. Understanding exposure concepts (specifically the CSA parameters and the holding period) is a prerequisite for this page.

Which parameters do the algorithms use?

Both algorithms read the CSA parameters of the netting set from the NettingAgreements table. See the data model for the field definitions.

Symbol	Parameter
$h$	Counterparty holding period, in days
$\theta_b$ , $\theta_c$	Bank and counterparty threshold
$m_b$ , $m_c$	Bank and counterparty minimum transfer amount
$A_b$ , $A_c$	Bank and counterparty independent amount constant
$k_b$ , $k_c$	Bank and counterparty independent amount scale factor
$F_b$ , $F_c$	Bank and counterparty independent amount floor
$I(T, s)$	Supplementary independent amount at time point $T$ in scenario $s$ , from the `IndependentAmounts` table

Both algorithms use the counterparty holding period

h

How is the collateral balance looked up in time?

For each reporting time point

T

, the algorithm values the netting set at the holding-period date

T - h

If $T - h$ is before the as-of date, the balance equals the initial collateral of the netting agreement, converted with the FX rate at $T$ . The exposure formulas below are not applied.
If $T - h$ is a date of the simulation grid, the algorithm uses the MtF value of the netting set at that date.
If $T - h$ falls between two grid dates, the algorithm linearly interpolates the MtF value between the two nearest reporting dates.

The algorithms evaluate reporting time points only. Time points that exist only for collateral evaluation serve as interpolation inputs.

How are currencies converted?

The CSA parameters are expressed in the CSA parameter currency. For each scenario

s

, the algorithm divides the MtF value at

T - h

by the FX rate at

T - h

to express it in that currency, and multiplies the resulting collateral by the FX rate at

T

to return to the cube base currency. FX rates for dates between two grid dates are linearly interpolated. In the formulas below,

R(s)

is the netting set MtF value at

T - h

in the CSA parameter currency, and

N(s) = \max(R(s), 0)

is its positive part:

R(s) = \frac{\text{MtF}(T - h, s)}{\text{FX}(T - h, s)}, \qquad N(s) = \max\bigl(R(s),\, 0\bigr)

The independent amounts

A_b

and

A_c

count as zero when

R(s) = 0

What is the total exposure under the Bilateral CSA algorithm?

The bilateral algorithm combines the counterparty-side and bank-side independent amount terms with the MtF value:

M_c(s) = \max\bigl(k_c \cdot N(s) + A_c + I(T, s),\; F_c\bigr)

M_b(s) = \min\bigl(k_b \cdot \min(R(s), 0) + A_b,\; F_b\bigr)

E(s) = R(s) + M_c(s) + M_b(s)

What is the total exposure under the Unilateral (Bank) CSA algorithm?

The unilateral algorithm uses only the counterparty parameters and the positive part of the MtF value:

M_c(s) = \max\bigl(\max(k_c \cdot N(s),\, 0) + A_c + I(T, s),\; F_c\bigr)

E(s) = N(s) + M_c(s)

How is the collateral call determined?

The collateral call

C(s)

turns the total exposure

E(s)

into a collateral amount, in the CSA parameter currency. A call is made only when the exposure exceeds the threshold by at least the minimum transfer amount. For the Bilateral CSA algorithm, the counterparty side is tested first, then the bank side:

C(s) = \begin{cases} E(s) - \theta_c & \text{if } E(s) > \theta_c + m_c \\ E(s) - \theta_b & \text{if } E(s) < \theta_b + m_b \\ 0 & \text{otherwise} \end{cases}

For the Unilateral (Bank) CSA algorithm, only the counterparty threshold and minimum transfer amount apply:

C(s) = \begin{cases} E(s) - \theta_c & \text{if } E(s) > \theta_c + m_c \\ 0 & \text{otherwise} \end{cases}

The collateral balance in the cube base currency is

C(s) \cdot \text{FX}(T, s)

How is collateralized exposure computed?

Both algorithms subtract the collateral balance

C^{\text{base}}(T, s)

from the netting set MtF value

\text{MtF}(T, s)

at time point

T

and take the positive part for the bank side and the negative part for the counterparty side:

E^{\text{coll}}_{\text{bank}}(T, s) = \max\bigl(\text{MtF}(T, s) - C^{\text{base}}(T, s),\; 0\bigr)

E^{\text{coll}}_{\text{cpty}}(T, s) = \min\bigl(\text{MtF}(T, s) - C^{\text{base}}(T, s),\; 0\bigr)

​Which parameters do the algorithms use?

​How is the collateral balance looked up in time?

​How are currencies converted?

​What is the total exposure under the Bilateral CSA algorithm?

​What is the total exposure under the Unilateral (Bank) CSA algorithm?

​How is the collateral call determined?

​How is collateralized exposure computed?

​Related pages