Discount Curves for Cross-Currency Swaps with Mandatory Breaks

Summary

The document asks how to discount the legs of a fixed-to-fixed cross-currency swap when its collateral currency changes at a mandatory break date. Without a break, its proposed setup discounts euro cash flows using the euro collateral curve and uses a cross-currency adjusted curve for the other currency under the same collateral agreement.

For a break that changes collateral from EUR to USD, the author considers constructing a piecewise discount curve for the EUR leg: use the EUR collateral discount factors through the break, then multiply the break-date factor by forward discount factors from a EUR-under-USD collateral curve for later cash flows. This reflects the distinct collateral regimes before and after the break. The document presents this as a question and tentative approach, not a confirmed pricing method; it gives no derivation, validation, or discussion of break exercise, payment timing, or other contract details that could affect valuation.

Key ideas

• Collateral currency determines the discounting framework for swap cash flows.
• A mandatory break can create different collateral regimes before and after its date.
• The proposed EUR leg curve preserves EUR collateral discounting up to the break.
• Post-break discounting is tentatively built from the break-date factor and forward factors under USD collateral.
• The proposed construction is unverified in the document and may depend on contract details.

Tags

# CCS Pricing with mandatory break clause


# CCS Pricing with mandatory break clause












Suppose I have to price a 5Y EUR-GBP fix-to-fix CCS. There is a EUR CSA (ESTR flat) in place with the counterparty. Additionally, there is a mandatory break clause after N years embedded in the swap. The applicable discount rate for this is in CCY3, which is different from EUR and GBP. How would I construct the applicable discount curves in this case?

Without break it is pretty clear. ESTR discounting the EUR cashflows and (EUR CSA) Cross Currency adjusted GBP curve for the GBP flows.

Edit Ok let's try to approach this. Suppose the following easy setup:

- 5Y fix-to-fix CCS GGB vs. EUR. Collateralized with EUR-CSA

- Mandatory break at 2Y with USD-CSA. Hence the remaining Swap is priced with CCS adjusted basis curves with USD collateral (GBP:USD and EUR:USD)

Let's concentrate on the EUR leg only. My best guess would be to construct a blended curve such that:

- Discount Factors up to 2y are exactly equal to ESTR discount factors (as any PV changes until break date are still collateralized under EUR-CSA)

- Discount Factor for 3y EUR cashflow would be 2y ESTR discount factor * Forward Discount factor (2 to 3 years) from the EUR:USD collateral curve (which we already constructed).

Does that makes sense?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.