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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?

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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.

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