Why a Swap’s Initial NPV Depends on Its Fixed Rate

Summary

The document explains why an interest rate swap may have a nonzero net present value at initiation even when its discount and forecast curves were built from the same market quotes. The accepted answer points to the fixed rate: the swap’s fixed leg must use the calculated fair rate for the initial value to be zero.

To make the swap’s NPV zero, retain the floating leg and rebuild the fixed leg using that fair rate. The example refers to a QuantLib valuation notebook, but the document does not provide the curve inputs, valuation details, or a numerical demonstration. Its explanation is concise and limited to the role of the fixed coupon; it does not discuss other sources of valuation differences.

Key ideas

• A swap built from market-quote curves need not have zero NPV if its fixed rate is not fair.
• The fair fixed rate is the rate that makes the swap’s initial NPV zero.
• Rebuild the fixed leg at the fair rate while keeping the floating leg unchanged to target zero NPV.

Tags

# NPV of Interest Rate Swap not coming to be 0 at initiation


# NPV of Interest Rate Swap not coming to be 0 at initiation












I am using the iPython notebook published by Gouthaman Balaraman at [http://gouthamanbalaraman.com/blog/interest-rate-swap-quantlib-python.html][1]

This is to value the Interest Rate Swap. I am intrigued that the NPV of swap is not 0 even if we were to be using the same quotes using which the discount curve (and same forecast curve) was constructed. Could someone kindly help me in understanding in what would it take to get the NPV = 0 in the example?

## Answer by Goutham (score 1, accepted)

https://quant.stackexchange.com/a/66064

The fair rate calculated in the above example is the rate to be used for fixed rate leg to yield 0 NPV. You would need to reconstruct the swap with the float leg as is but a fixed leg with fair rate from above. That should yield a 0 NPV for the swap.

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