## IBOR transition: impacts of the SOFR discounting switch

## Perspectives

# IBOR transition: impacts of the SOFR discounting switch

Thu 19 Nov 2020

An important milestone in the IBOR transition is the change in rates used by LCH and CME for discounting and Price Alignment Interest (PAI) calculations for USD OTC cleared swaps. Indeed, on October 16,^{ }2020, they moved from using the daily Effective Federal Funds Rate (Fed Funds) to the Secured Overnight Funding Rate (SOFR) for these calculations. A similar change occurred in July this year when the rate used in discounting and PAI on EUR-denominated Swap Clear products was changed from Euro Overnight Index Average (EONIA) to Euro Short-Term Rate (€STR). Considering that these Central Clearing Counterparties (CCPs) are responsible for more than 50% of all interest rate swaps (by notional), this is an important change and will lead to a gradual shift in discounting practices in the market.

### What’s changing

#### CCPs SOFR discounting switch

Driven by the benchmark reform, existing IBOR benchmark rates will cease to be published. They will be replaced by alternative risk-free rates (RFR) like the Secured Overnight Financing Rate (SOFR) in the case of the US dollar (USD) market. A crucial step in the successful transition of the swap market to new RFRs is the switch in discounting curves used by CCPs.

From end of day October 16, 2020, the two big clearing houses LCH and CME started using SOFR instead of the Fed Funds rate for the PAI for USD collateralised transactions. PAI is the rate of interest paid on the cash collateral posted as variation margin on the cleared derivatives. In order to maintain consistency between margin/collateral funding versus discounting of derivative cash flows, derivative transactions are valued using discount curves consistent with the PAI. Indeed, cleared swaps were discounted at the Fed Fund OIS rate (called the OIS curve) since the PAI was the Fed Funds rate. In order to move the market towards SOFR, CCPs have now begun using SOFR for PAI and collateral valuation. This means that SOFR is being used to discount all cleared trades from October 16, 2020. The move is expected to increase liquidity in the SOFR based derivatives.

#### What about Bilateral contracts

Non-centrally cleared (bilateral) financial derivatives are typically traded under Credit Support Annexes (CSAs). A CSA stipulates the rate of interest paid on the cash variation margin. Most existing CSAs will specify the Fed Funds rate as the rate of interest to be paid on the variation margin. Therefore, the bilateral trades will continue to be discounted at the OIS (Fed Funds) curve in the near term. It is, however, possible that new CSAs may start referencing the SOFR as the interest rate and there is an expectation that CSAs may be amended to replace Fed Funds with SOFR as we move closer to the deadlines for IBOR transition. In fact, large banks have already started the transition and have amended their systems to use SOFR discount curves.

This means that valuation systems should be capable of valuing derivatives based on both Fed Funds OIS and SOFR discount curves and traders should be able to measure the impact of the discounting switch on their books by valuing positions under both curves. Similarly, risk managers will need to measure the impact of switching the discount curves on the risk weighted assets (RWAs) for the calculation of the market risk regulatory capital.

#### Impact on SOFR Liquidity

It is expected that the discounting switch will lead to an increase in trading activity in SOFR linked derivatives as firms move to hedge their discounting risk. According to LCH[1] and CME[2] monthly trading numbers for October the discounting switch to SOFR has increased trading in SOFR linked swaps. At LCH the monthly swaps volume (in terms of Notional) increased from USD 381.64 billion in September to USD 628 billion in October while CME reported an increase from USD 21.7 billion to USD 98.2 billion.

### Assessment of the impact of SOFR discounting switch on valuation

#### Impact on pricing models

The SOFR discounting switch triggers a pricing model change and risk managers are required to perform an impact analysis to measure the impact of the switch. They must also provide the regulator with updated documentation of the model change and detailed reports on the results of the impact analysis. The higher the impact, the earlier the notification should be: if the impact is considered immaterial, it can be a simple notification after implementing the model change, but if the impact is considered significant or material[3], it can also be an approval request.

#### Constructing SOFR Discounting Curves

Table 1 specifies the instruments used by both the clearing houses for constructing their SOFR curves after the transition. The choice of instruments is governed by liquidity. At the CME, SOFR futures were launched in May 2018 and are the most liquid products that have SOFR as an underlying. Fed Funds-SOFR Basis swaps are used for the remainder of the curve as they are the most liquid OTC product. LCH built the SOFR discount curve from SOFR-Fed Funds basis swaps that were auctioned as part of the discounting switch[4].

Table 1 Instruments used for constructing the SOFR curve by CCPs

It is expected that as the market for SOFR derivatives becomes more liquid, more SOFR based instruments will be included in construction of the discount curve. These instruments include SOFR swaps (overnight index swaps linked to the SOFR) and Libor-SOFR basis swaps.

In order to fair value derivatives after this switch in discounting practice, a valuation platform should have the ability to bootstrap these SOFR linked instruments and construct the SOFR discount curve. Bootstrapping the SOFR futures contracts will be challenging since these are based on the daily compounded backward-looking rates. We have modelled the SOFR futures under the forward market model, allowing us to calculate the convexity adjustment for SOFR futures and bootstrap the SOFR curve. The model is based on an extension of the Libor Market model (LMM) and enables us to model both forward looking and backward-looking rates under a single framework.

Based on our understanding of SOFR modelling and the IBOR transition, we have performed the required implementation to be able to compute the valuation of IR derivatives based on both RFR linked market data and current OIS discount curves that we present in the next section.

#### Assessment of the discounting switch on IR Swap valuation

In order to assess the impact of the SOFR discounting switch, we use real market data from Bloomberg as of September 30, 2020 and construct SOFR discount curve to value interest rate swaps. Table 2 shows the difference in discount factors between the OIS (Fed-Funds) curve and the SOFR discount curve as of September 30, 2020. As expected, the SOFR discount factors are higher than the OIS curve (since the SOFR is a secured rate, it is expected to be lower than the Fed Funds rate). We find that for lower tenors (0-3 years), the difference in discount factors is immaterial. However, for tenors greater than 7 years the discount factor difference is more than 15 bps, while for tenors greater than 20 years the difference is more than 100 bps. Thus, we can conclude that the change in discount curves can have a significant impact on present values for longer dated cash flows.

Maturity | SOFR | Fed Funds OIS | Difference in Bps |

6 M | 0.9996 | 0.9996 | 0 |

12 M | 0.9994 | 0.9994 | 0 |

18 M | 0.9993 | 0.9993 | 0 |

2 Y | 0.9993 | 0.9993 | 1 |

3 Y | 0.9989 | 0.9987 | 2 |

4 Y | 0.9971 | 0.9967 | 3 |

5 Y | 0.9935 | 0.9928 | 7 |

7 Y | 0.9807 | 0.9791 | 16 |

10 Y | 0.9527 | 0.9497 | 30 |

12 Y | 0.9313 | 0.9266 | 47 |

15 Y | 0.8993 | 0.8922 | 71 |

20 Y | 0.8481 | 0.8370 | 111 |

25 Y | 0.8029 | 0.7894 | 135 |

30 Y | 0.7662 | 0.7468 | 194 |

40 Y | 0.7186 | 0.6920 | 266 |

50 Y | 0.6944 | 0.6618 | 325 |

Table 2: Discount Factors from Fed Funds OIS Curve and new SOFR curves as of September 30^{th}, 2020

To assess the impact on valuations, we price a range of USD interest rate swaps using the SOFR discount curve and observe the change in mark to market. We calculate the P&L impact for a swap as the difference between the present value of future cash flows under the Fed Funds discount regime versus the SOFR discount regime:

where *DF _{i}^{SOFR}* is the discount factor from the SOFR curve and

*DF*is the discount factor from the existing Fed Funds OIS curve. Note that for this analysis we hold the

_{i}^{Fed Funds}*Future cash Flows*constant[6] and only change the discount curve. This is also the approach used by both LCH[7] and CME[8] to calculate their clients’ compensation amounts from the SOFR discounting switch.

_{i}Figure 1 shows the P&L impact for interest rate swaps of varying maturities (receive fixed v/s pay USD Libor 3M) due to the shift to the SOFR discount curve as of September 30, 2020. All swaps have a notional of 10M USD. We vary the fixed rate for the swaps as described in the table below:

Swap Type | Description |

At-the-money (ATM) | Swaps with fixed rate = par rate i.e. swaps that are currently trading with a net present value (NPV) of close to 0 |

In-the-money 1% (ATM +1%) | Swaps with fixed rate = par rate + 1% |

In-the-money 2% (ATM +2%) | Swaps with fixed rate = par rate + 2% |

We observe that for ATM swaps, the impact of SOFR discounting is immaterial. This is because both the pay and receive cash flows are impacted proportionally by the SOFR DFs. The P&L impact is slightly negative because the SOFR discounting impact is greater for long tenors (as shown in Table 2). For receive-fix pay-floating ATM swaps, the net cash flows are negative in the longer tenors (since projected floating Libor rates increase with longer tenors for an upward sloping forward curve).

We also see that the impact of SOFR discounting depends upon the moneyness of the contracts and increases as present value of contracts increases. This is seen in the impact of the discounting switch for in-the-money (ITM) swaps. ITM swaps (receiver swaps for which fixed rate is greater than the par swap rate[9]), have a positive mark to market due to positive net cash flows. Since SOFR discount factors are greater than those from the Fed Funds OIS curve, the net present value of ITM swaps is greater for the SOFR curve than for the OIS curve and hence the P&L impact is positive. As expected, the P&L increases with the maturity of the swap contracts since the SOFR discounting impact is higher for longer tenors.

Figure 1: P&L impact of SOFR discounting on USD Receive Fixed Interest Rate Swaps.

Note that the behaviour for OTM swaps will be reverse, i.e. the P&L impact will be negative.

### Conclusion

It is observed that the switch to SOFR discounting can have significant impact on the valuations for longer dated instruments. Understanding the full effect of SOFR discounting will be important for all market participants, and Mazars Quantitative Solutions have carried out extensive research in SOFR modelling and understanding the quantitative impacts of IBOR transition[10]. Our valuation tools can be customized to use relevant market data for SOFR based instruments, create new discount curves, and perform valuations, enabling us to assess the impact of the IBOR transition on market portfolios.[11].

For further details on Mazars’ IBOR tool, **click here**.

**This article was written by Mariem Bouchaala and Akhilesh Bansal.**

[1] https://www.lch.com/services/swapclear/volumes/rfr-volumes ; [2] https://www.cmegroup.com/trading/interest-rates/cleared-otc-sofr-swaps.html ; [3] For further details on how to assess the materiality of changes to internal market risk models, refer to EU 2015/942 ; [4] LCH provided ‘risk compensation’ in the form of Fed Funds versus SOFR basis swaps. The purpose of these compensating swaps is to reverse the change in discounting risk resulting from the update to the discounting curve. Clients could opt-out of these compensating swaps and their positions will be liquidated subject to a close-out process using an auction, to be run by LCH. [5] SR1 and SR3 are CME codes for 1-month and 3-month serial futures contracts respectively; [6] The future floating cash flows are calculated from the Forward Libor curve. The Libor forward curve is stripped using the Fed Funds OIS discount curve as part of dual curve stripping methodology. However, for our analysis, we keep the forward rates constant when switching over to SOFR discounting. As mentioned above, this approach is also followed by the CCPs.[7]https://www.lch.com/system/files/media_root/SOFR%20discounting%20for%20LCH%20website%20June2020.pdf ; [8] https://www.cmegroup.com/trading/interest-rates/files/cme-sofr-discounting-and-pa-transition-whitepaper.pdf ; [9] ITM swaps can also be payer (pay-fixed) swaps where the fixed rate is less than par swap rate. [10] For more information on modelling of SOFR risk factors, please click here. [11] For further details on Mazars’ IBOR tool, click here.