ImpYC CSA Disc
ImpYC CSA Disc is a direct subtype of ImpYC
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TYPE INCLUSION RELATIONSHIPS
AVAILABLE FUNCTIONS
AVAILABLE CREATE FUNCTION KEYS
TYPICAL OBJECTS OF TYPE ImpYC CSA Disc
This type represents the input data required to build a target yield curve (i.e. an object of type Yield Curve), referred to as TgtCcyColBCURVE below, that represents the curve of discount factors that must be used to discount cash flows denominated in a given currency TgtCcy when they are collateralized and the collateral is held in a different target currency ColB
Technically, the TgtCcyColBCURVE is created by feeding an object of the ImpYC CSA Disc type as value next to the key Market Data in the formula that creates the TgtCcyColBCURVE
The following three curves are assumed known and must be supplied as input:
1) The target currency curve, referred to as TgtCcyColACURVE below, used to discount cash flows denominated in TgtCcy and collateralized in some given source collateral currency ColA
2) The source currency curve, referred to as SrcCcyColBCURVE below, used to discount cash flows denominated in some source currency SrcCcy and collateralized in ColB
3) The source currency curve, referred to as SrcCcyColACURVE below, used to discount cash flows denominated in SrcCcy and collateralized in ColA
Note that under the usage of this type, the arrays reported by the keys _Curve Pegs and _Curve Values refer only to the curve SrcCcyColACURVE
The most common case is the two-currency case when the collateral currencies equal the curve denomination currencies so that:
ColB = SrcCcy and ColA = TgtCcy
Then only the two currencies SrcCcy and TgtCcy are involved and the output curve TgtCcyColBCURVE becomes effectively the TgtCcy basis curve that must be used to discount TgtCcy-denominated but SrcCcy-collateralized cash flows.
Also the input curves are then interpreted as follows:
1) The curve TgtCcyColACURVE is the local TgtCcy discounting curve, typically bootstrapped from the local TgtCcy OIS market rates.
2) The curve SrcCcyColBCURVE is the local SrcCcy discounting curve, typically bootstrapped from the local SrcCcy OIS market rates.
3) The curve SrcCcyColACURVE is the SrcCcy basis curve that must be used to discount SrcCcy-denominated but TgtCcy-collateralized cash flows and typically bootstrapped from cross currency swap market basis spreads with the help of the Yield Curve Fxb type.
Here is an example of the two-currency case:
Consider the valuation of a bespoke cross currency swap between USD and GBP, where the collateral is held in GBP.
If we assume that the swaps quoted in the market are collateralized in USD, one can first build a basis GBP discounting curve by applying the type Yield Curve Fxb on the available market basis spreads.
Let's refer to the above curve as the GBP BASIS CURVE
Note that the creation of the GBP BASIS CURVE would require the knowledge of the local discounting curves in USD and GBP, i.e. the curves implied by the local OIS markets.
Let's refer to these two curves as USD LOCAL CURVE and GBP LOCAL CURVE, respectively.
The valuation of the most common USD-collateralized swap proceeds as:
1) calculating the USD-denominated NPV of all USD cash flows by discounting them with the USD LOCAL CURVE and adding up the produced numbers
2) calculating the GBP-denominated NPV of all GBP cash flows by discounting them with the GBP BASIS CURVE and adding up the produced numbers
3) converting one of the results above to the other currency using the known spot fx rate so that both numbers refer to the same currency and thus can be added together to quote the final NPV in the desired currency.
The valuation of the bespoke GBP-collateralized swap would have to follow similar steps, but the problem is that a USD BASIS CURVE is not available.
The type ImpYC CSA Disc can be used to produce the required USD BASIS CURVE, as follows:
Set TgtCcy = USD , SrcCcy = GBP , ColB = GBP and ColA = USD
Then TgtCcyColBCURVE corresponds exactly to the - yet unknown - USD BASIS CURVE.
The - assumed as known - SrcCcyColACURVE is the known GBP BASIS CURVE
The - assumed as known - TgtCcyColACURVE and SrcCcyColBCURVE are the known USD LOCAL CURVE and GBP LOCAL CURVE, respectively.
After the USD BASIS CURVE has been built, the valuation of the bespoke GBP-collateralized swap would proceed by:
1) calculating the USD-denominated NPV of all USD cash flows by discounting them with the USD BASIS CURVE and adding up the produced numbers
2) calculating the GBP-denominated NPV of all GBP cash flows by discounting them with the GBP LOCAL CURVE and adding up the produced numbers
3) converting one of the results above to the other currency and add the final numbers together
A less common case is the three-currency case when the target collateral currency equals the source curve denomination currency, i.e. when:
ColB = SrcCcy
Then only the three currencies SrcCcy, TgtCcy and ColA are involved and the output curve TgtCcyColBCURVE is exactly as in the above two-currency case and equals the TgtCcy basis curve that must be used to discount TgtCcy-denominated but SrcCcy-collateralized cash flows.
The difference lies in the input curves that are now interpreted as follows:
1) The curve TgtCcyColACURVE is the TgtCcy basis curve that must be used to discount TgtCcy-denominated but ColA-collateralized cash flows.
2) The curve SrcCcyColBCURVE is the local SrcCcy discounting curve.
3) The curve SrcCcyColACURVE is the SrcCcy basis curve that must be used to discount SrcCcy-denominated but ColA-collateralized cash flows.
The three-currency case can be useful when there exist no liquid traded instruments the link directly the currencies SrcCcy and TgtCcy.
An example could be the valuation of a CAD-collateralized bespoke cross currency swap between GBP and CAD
From the CAD-counterparty perspective, the natural setting would be:
TgtCcy = GBP , SrcCcy = CAD , ColB = CAD
Invoking the two-currency case by setting ColA = GBP would not be tenable because this would require the input of curves implied by market basis spreads of GBP-collateralized GBP-CAD cross currency swap that are not liquidly traded.
Given the fact that the market trades USD-collateralized GBP-USD swaps and USD-collateralized CAD-USD swaps, the solution is to opt for the three-currency case by choosing USD as the ColA currency.
The input curves would then be as follows:
1) The curve TgtCcyColACURVE becomes the GBP BASIS CURVE
2) The curve SrcCcyColBCURVE is the local CAD discounting curve that may be referred to as CAD LOCAL CURVE
3) The curve SrcCcyColACURVE becomes the CAD BASIS CURVE, bootstrapped directly from the market CAD-USD swap basis spreads.
The curve construction methodology is definbed in Method