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Delta Sensitivity of Interest Rate Swap – Part II

Learn more about Delta Sensitivity with Part I.

Results

Zero Delta

The following figure and table show zero delta vector along the maturities.cc. But this pattern is not absolute and is subject to the change of market environment because these days shows ultra lower interest rates.

Market Delta

The following figure and table show market delta vector along the maturities. Like zero delta, a meaningful value of delta is only observed at maturity since delta at maturities less than IRS maturity (3-year) is considered a zero. Like zero delta, this pattern is also not absolute and is subject to the change of market environment from the same reason.

Intuition behind IRS delta

Let’s assume the maturity of IRS is 3-year.

In both case of zero and market delta of IRS, we can observe the peak of delta at the IRS maturity. Increase in the interest rate has two effects. Firstly a higher interest rate decreases a discount factor and increases variable cash flows. These two effects have a trade-off.

Secondly, forward rates, which determine future cash flows show the following up and down pattern (we use 25bp up for the clear visual inspection and illustration) because the next swap rate is determined at market value, of which maturity is beyond the bumping maturity. Therefore there are positive and negative effects on future cash flows at the bumping time and the next time.

But at maturity, there is only positive effect on future cash flows because the successive negative effect takes place beyond the maturity of this IRS.

To be more specific, let’s compare the Aqua and Yellow colored lines, which represent the forward rate curve with 2-year and 3-year swap rate bumping up respectively. We can observe that as the 2-year swap rate is bumped up, a downward movement of forward rate at time 2.25-year is following the upward movement of it at time 2-year. But in case of 3-year bumping, there is only upward movement of forward rate at time 3-year.

Conclusion

From this post, we have calculated delta sensitivities of IRS. In this example, two methods do not show some significant differences. But this result is not general because market Greeks permit interactions between market variables but zero Greeks does not (or little).

For example, in case of a Libor 3×6 basis swap, when Libor3M swap rates are changed, Libor6M zero curve is also changed. But there is little or no interaction effect in the case of zero Greeks. Therefore, it is advised for you to investigate the full effect of Greeks calculation in many cases.

For additional insight on this topic and to download the R scripts, visit https://kiandlee.blogspot.com/2021/07/delta-sensitivity-of-interest-rate-swap.html.

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