Monday, 29 October 2018

LIBOR Fallback transformers - magnified view on risk

In this new post, following questions by readers, we come back to the delta ladder associated to the different fallback options. In the LIBOR Fallback transformers - PV and Delta post, we have presented the risk associated to the first coupon of the forward swap. The coupon starting in 6 months and ending in 9 months. In the case of Overnight Spot fallback option, from the delta ladder, it looks like the the sensitivity of a 3-month instrument on the "wrong" period, while from the description it should be a 1-day risk starting at the fixing. Actually both descriptions are correct, but the delta ladder one is looked at with the wrong glasses.

The delta ladder using tenors with 3-month gaps is a good way to look at the risk when the risk is on 3-month benchmarks. When we look at single overnight fixings, like in the case of the Spot Overnight fallback option, you don't see clearly through those glasses. To see to which extend the glasses are deforming the view of the risk, we have recreated the delta ladder with weekly tenors up to 40 weeks (~ 9 months). Obviously there is no liquid market of weekly swaps up to 40 weeks, but we have created synthetic quotes for them and calibrated (synthetic) curves with those nodes and computed the sensitivities at each of them (by Algorithmic Differentiation, indeed)

If we look at the OIS Benchmark risk, nothing is changing, there is some risk at 26 weeks (6 months) and some risk at 39 weeks (9 months). If we look at the Overnight Spot option, the picture is very different, there is very large sensitivities with opposite signs at 25 and 26 weeks (note that due to the T+2 convention for OIS, the starting date of the LIBOR period is not the same as the starting date of the ON period). Nothing like a 3 months risk. There is clearly a very short term risk around that date. There is also a very small discounting risk at the payment date (39 weeks), but it is so small that you would be excused if you had not noticed it. Finally we look at the Compounding Setting in Advance case. We see large risks at 12 weeks and 26 weeks, corresponding to the period where the rate is compounded and a very small risk at the 39 weeks for the discounting of the payment.

OIS Benchmark Spot Overnight Compounding in Advance

Note that the total (parallel)  delta is almost the same for all options.

Looking at the reports, you will say: "Nobody is producing those kind of reports with weekly (or worst daily) risk". And I agree with you that nobody is doing something like that today. But if the Overnight Spot option is selected by ISDA, tomorrow everybody will be forced to do something similar. Risk reports with daily nodes will be required, specially in periods where the central banks are likely to hike (or cut) rates.

The same issue can be seen for the large test portfolio used previously.  Instead of showing it with a risk report as above, we are showing it by plotting the daily risk sensitivities. The graph below represent the LIBOR sensitivities at each fixing date. Each line represent the change of value of the portfolio for a change by one basis point of the forward rate fixing on that date. This is a risk report with daily precision. We displayed only a little bit more than 4 years and not the 50 years of sensitivities in the test portfolio. Those LIBOR-3M sensitivities are transformed by the fallback with Spot Overnight option to overnight sensitivities. Where there was before some averaging on a 3-month period, there is now a spike on a unique day. No risk compensation by overlapping periods is achieved anymore.

  1. Fallback transformers - Introduction
  2. Fallback transformers - Present value and delta
  3. Fallback transformers - Portfolio valuation
  4. Fallback transformers - Forward discontinuation
  5. Fallback transformers - Convexity adjustments
  6. Fallback transformers - magnified view on risk

Don't fallback, step forward!

Contact us for our LIBOR fallback quant solutions.