Setting Hypothetical Derivative Rates for Cash Flow Hedge Accounting
Summary
The document discusses how to set the fixed rate on a hypothetical derivative used to assess a cash flow hedge of a foreign currency liability with a cross-currency swap. The hypothetical derivative should start at zero fair value and have cash flows that match the hedged liability. One method is to solve for the pay-leg rate that makes the swap value zero, using overnight discount curves and excluding cross-currency basis. An approximation transfers the receive-leg coupon’s spread over its par rate to the pay-leg currency’s par rate; tenor basis adjustments may refine that estimate.
A second response describes a different treatment: when the real hedge began near zero value and terms match, use the same fixed rate for the hypothetical derivative, then include CVA in the hedging instrument’s later valuation rather than changing the hypothetical rate. The notes identify credit and cross-currency basis as potential sources of ineffectiveness, with basis treated separately as a cost of hedging. These are practitioner explanations, not a full accounting standard analysis; the appropriate setup depends on hedge terms and applicable accounting policy.
Key ideas
- The hypothetical derivative is structured to match the hedged liability’s cash flows and have zero initial fair value.
- A pay-leg rate can be found by solving for a zero-value swap using overnight discount curves while excluding cross-currency basis.
- An approximate rate transfers the receive-leg coupon’s spread over par to the pay-leg currency’s par rate.
- Tenor basis adjustments can refine the approximate rate.
- An alternative approach keeps matched fixed rates and includes CVA directly in later hedging-instrument valuation.
Tags
Full text
# Cash Flow Hedge Accounting # Cash Flow Hedge Accounting In the context of hedging a fixed rate foreign currency liability with a receive-fixed pay-fixed CCS is known that in order to assess the effectiveness of a cash flow hedge the ratio of the change in the fair-value of the hedging instrument and change in the fair-value of the hypothetical derivative should be between 80% and 125%. The hypothetical derivative has the same terms of the hedging instrument, but it doesn't take into the CVA, so it has an additional spread to the pay-fixed rate (some bp). Also, the hypothetical derivative, at inception, has zero fair-value. How can this spread be calculated in order to meet the requirements of the hypothetical derivative? ## Answer by Ami44 (score 1) https://quant.stackexchange.com/a/46649 I assume the cross currency basis spread is separated. Your hypothetical derivative has a value of zero and the cashflows of the receive leg are matching your liability. That is enough to determine the interest rate on the pay leg. One method to determine it, is to vary the rate on the pay leg and calculate the value of the swap until it is zero. To calculate the value, discount with the overnight curves in the respective currency and ignore the cross currency basis spread. An easier method to determine the rate on the pay leg is to calculate the spread over the current swap par rate on the receive side and apply the same spread to the pay leg. For example if your liability has 5% interest and the par rate in that currency is 3%, than you are 2% over par. If the par rate in the pay leg currency is 1.5% than we get an rate of 3.5% on the pay leg. This is an approximation that can be further refined by correcting for tenor basis spreads. If your swap pays every 3 Month, you can apply the 3M/OIS Spread for each Currency to each leg. ## Answer by soju (score 1) https://quant.stackexchange.com/a/81183 From my experience; assuming the hedging instrument started sufficiently close to zero, the hypothetical (ie hedged item) fixed rate would be equivalent to the hedging instrument. At any future remeasurement date, you add CVA to the hedging instrument value and do not for the hypothetical. In this way, you don't account for the CVA by using a different rate on the hypothetical, but rather you account for it directly by adding it to the swap. Therefore, assuming matched terms, any ineffectiveness should be driven by credit as well as xccy basis - the latter of which is carved out and reported separately as a cost of hedging.
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.