As for previous blogs, we do it first for a single swap and then for our large test portfolio. We look at the timing adjustment for the Spot Overnight option.
For the adjustment we have selected the one-factor Hull-White model and the corresponding adjustment as described in our Quant Perspective on IBOR fallback Proposals.
In this case, we have selected a 10Y swap starting in 6 months. The coupon is 2.5% and the adjustment spread is 25bps. For the model parameters, we have taken round figures with the mean reversion at 2% and the (normal) volatility at 100bps.
The impact on the swap par rate is 1.2bps. This may look like somehow smaller than what is displayed in Figure 4 of the quant perspective, but in the paper the adjustment was for a single payment, while here it is for the full swap. The adjustments are somehow averaged between all the payments on the 10Y tenor.
If if lengthen the swap's maturity to 30Y, the impact is 2.4bps.
At the level of the delta, the difference between the adjusted and non-adjusted figures are very small.
|Discounting delta||Adjusted delta|
If we look at the impact on a full portfolio, this can be important. For a test portfolio with 1000 swaps (slightly different from the installment 2), the PVs without and with timing adjustment are
The large difference comes from large positions in the very long term part of the curve for the LIBOR curve.
- 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
- Fallback transformers - Risk transition
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