Typically, an interest rate swap whose fixed rate payment substantially deviates from currently prevailing coupon rates on debt instruments with similar times to expiration. An adjustment to the net present value of this swap needs to be made, and therefore the counterparties would be required to exchange an extra amount whether at inception or expiration. The extra payment is technically called a buy up or a buy down. The extra sum will be paid up front by one counterparty to another. However, the floating rate doesn’t deviate from a rate applicable on an at-market swap.
The off market coupon swap is also called an off-market swap and an adjustment swap.
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