The portfolio we used for the examples is a portfolio of 1,000 USD swaps semi-randomly generated with different maturities, rate levels and conventions. Some trades are Fixed v LIBOR 3M, some OIS and some basis Overnight V LIBOR 3M.

### Present value

In the previous blog, we have seen that at a single trade level, the difference between the different options are not very large. On a portfolio level the result may be different. For the portfolio we have tested, we obtained the following results:

We have used a fixed spread of 25 bps. What we want to analyse is not only the difference between the legacy portfolio and the portfolio after fallback, we know that it will depend strongly on the spread selected, but also the difference between the different options.

The first test was run with curves calibrated with linear interpolation on the zero-rates. We see that, as expected, the

*Compounded Setting in Arrears*and the

*OIS Benchmarks*options gives almost the same value. Other options give relatively large differences, up to 160m on this large portfolio.

### Computation time

A natural question, looking at all those options and the present value and sensitivity computations, is to know how much computation power is required to obtain those results. The answer is probably less than what most would expect. In the first test for the 1000 trades portfolio above and for the legacy description plus the 4 options analysed, the total computation time for the PV and all the delta ladders was around than 2 seconds (to be exact, 250ms to load the portfolio from a csv file and 1900ms to generate the 5 versions of the swaps and compute PV and delta for all versions; time computed on the author's laptop; time for other interpolation mechanisms in next section).

### Interpolation

As the options change the way the rate is computed, we can expect the interpolation mechanism to have an impact. In the quant perspective, we have described how the interpolation mechanism has an impact on the forward spread, there is a lot of literature on the impact of interpolation on forward rates, and here we check the impact of the fallback option on the PV (through the forward rates) and see how much difference there is between the options depending on the interpolation mechanism. The interpolation schemes we have used are linear on the zero-rates, monotone cubic spline on the discount factors, natural cubic spline on the zero-rates and log-linear on the discount factors.

For the three options OIS Benchmark, Compounded in Arrears and compounded in Advance, there is a significant difference with LIBOR and between them, but the difference does not change significantly with the interpolation mechanism. This is not really surprising as each of them has an averaging mechanism on the coupons and the portfolio has a decent diversification in term of maturities and payment schedules. All yield curves are calibrated to the market and this is sufficient to have a relatively stable impact. In the case of the Spot Overnight option, the story is different. In this case, the rate selected for the fallback is a single day rate taken outside of the LIBOR period. The averaging and diversification does not work as well. The impact of the fallback can vary from almost nothing to more than 100m. It would certainly be possible to create portfolios where those impacts are even larger, just by selecting coupon fixing dates at special dates.

- Fallback transformers - Introduction
- Fallback transformers - Present value and delta
- Fallback transformers - Portfolio valuation
- Fallback transformers - Forward discontinuation
- Fallback transformers - Convexity adjustments
- Fallback transformers - magnified view on risk

Don't fallback, step forward!

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