How Forward Rates and Discounting Shape Swap Basis Risk

Summary

The exchange examines two claims about basis movements and the value of a receive-fixed, pay-one-month-LIBOR swap. It explains that a widening one-month versus three-month LIBOR basis does not have a single implication: the result depends on which tenor’s forward rates move. If one-month forwards fall while three-month forwards are unchanged, the swap gains value; if only three-month forwards rise, the swap may be unaffected. The benchmark convention can help explain why traders sometimes assume one particular rate moves.

It also discusses OIS discounting. For a swap initiated at market with zero present value, a change in discount rates has little effect on value. A positive-value swap can benefit when the discount rate falls, such as when LIBOR/OIS spreads widen while LIBOR stays constant. These are conditional explanations, not universal rules: valuation depends on the swap’s existing value and on how the underlying forward curves and discount curve change.

Key ideas

• A change in a tenor basis does not determine swap profit without knowing which forward curve moved.
• A fall in one-month LIBOR forwards can help a receive-fixed, pay-one-month-LIBOR swap if three-month forwards remain unchanged.
• A rise in three-month forwards alone may leave that swap’s value unchanged.
• Discount-rate changes have little effect on a newly entered, zero-value swap.
• A positive-value swap may gain when its discount rate falls, all else equal.

Tags

# Beginner question about basis risk


# Beginner question about basis risk












new to the area, and had a question about basis risk.

If I entered into a receive fixed pay 1mo Libor swap, why is it good for me if the 1x3 month Libor widens and bad for me when it tightens. Also if I am OIS discounting, why is it good for me if the OIS/3Mo Libor basis widens and bad for me when it tightens.

Thanks in advance for your help.

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/30940

I don't agree with either statement. Taking the first statement , if you receive fixed/pay 1m libor , and the 3m/1m basis widens. There are two ways this can happen (I) the forward rates for 1m libor go down and the forward rates for 3m libor stay the same. In this case you make money. But also (II) the forward rates for 3m libor could go up and the forward rates for 1m libor stay the same. In this case you make no money. I am guessing that whomever told you that was assuming that the case (I) applies, since most swaps traders use 3m libor swaps as a benchmark.

In the second statement, if you have just done a swap at market, such that its present value is zero , then changing the discount rate has little effect on its value. The statement would be generally true if the swap were "in the money", meaning having positive value to you. Then if the discount rate is lowered , by libor/iOS spreads widening when 3mo libor stays the same , then you would make money.

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