# LIBOR Fallback and Quantitative Finance

^{1}

^{2}

## Abstract

**:**

## 1. Introduction

^{®}, the association which publishes the ISDA Master Agreement used by most financial institutions, has issued two consultations on the subject: ISDA (2018b) and ISDA (2019). However, a legal challenge does not mean that it can be solved by pure rewording without taking the underlying reality of the derivative’s market into consideration. There are constraints on the way the contracts can be drafted and amended imposed by the financial reality that those contracts represent.

## 2. Fallback, Notations and Vanilla Products

**Theorem**

**1.**

## 3. Fallback and Expected Value

## 4. Adjusted RFR

**Theorem**

**2.**

**Proof.**

## 5. Adjustment Spread

## 6. Options and Hedging

^{®}12, but there is no derivative trading currently on those indices and there is also no practical possibility to extract any information from them.

## 7. Conclusions

## Funding

## Conflicts of Interest

## Abbreviations

ISDA | International Swaps and Derivatives Association |

LIBOR | London InterBank Offered Rate |

EFFR | Effective Federal Fund Rate |

SOFR | Secured Overnight Financing Rate |

FRA | Forward Rate Agreement |

OIS | Overnight Indexed Swap |

## References

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1 | We use the term LIBOR to designate benchmarks related to interbank lending. Sensu stricto, the term LIBOR is restricted to the benchmarks administered by IBA and fixing in London. By abuse of language, we extend it in this note to other similar benchmarks such as EURIBOR, TIBOR, BBSW, etc. |

2 | Thanks to Andrea Macrina for pointing this way to describe the measurability problem. |

3 | |

4 | Letter available at https://www.isda.org/a/Y6SME/April-2019-Letter-to-FSB-OSSG.pdf. |

5 | Document available at https://www.newyorkfed.org/medialibrary/Microsites/arrc/files/2019/FRN_Fallback_Language.pdf. |

6 | See the administrator website at https://www.theice.com/iba/ice-swap-rate. |

7 | Text available at https://www.isda.org/a/Y6SME/April-2019-Letter-to-FSB-OSSG.pdf. |

8 | The exact wording is: ISDA to work with The Brattle Group and other external experts to analyse and perform sensitivity analysis on the “historical mean/median approach” to the spread adjustment (without input from ISDA working groups or market participants during this time period given the sensitivity of the parameters). |

9 | The target replacement for USD-LIBOR is SOFR, but the liquidity of SOFR based swaps is currently very limited and it is proxied here with EFFR. The difference in the current market is a couple of basis points. |

10 | Similar results have been obtained for the CHF, GBP markets and and USD-LIBOR-6M. The CHF data are described in Pomberg and Willems (2019). The GBP and some USD data are not depicted in this note but can be found on the author’s blog at http://multi-curve-framework.blogspot.com/. |

11 | See description at https://www.theice.com/iba/Bank-Yield-Index-Test-Rates. |

12 |

**Figure 1.**Representation of the dates associated to a LIBOR fixing and a LIBOR coupon in a vanilla IRS.

**Figure 4.**Historical time series for USD-LIBOR-3M and EFFR compounded on three-month periods. Running mean and median are for 5-, 7 -and 10-year look back periods and different announcement dates.

**Figure 5.**Historical time series for long tenor (30-year) basis swaps USD-LIBOR-3M/EFFR around the ISDA consultation period. The red vertical line is the consultation result date. The different thin lines are the author’s estimates using scenarios with different methodologies.

**Table 1.**Spread between the different LIBOR indices and overnight composition. The spreads at the different dates are the market spreads for 30-year tenor basis swaps similar to those reported in Figure 5 for USD-LIBOR-3M. The ranges represent the author’s estimates for the different scenarios.

Index | July 2018 | November 2018 | May 2019 | Range |
---|---|---|---|---|

USD-LIBOR-3M | 45 | 38 | 25 | (18–28) |

USD-LIBOR-6M | 57 | 50 | 35 | (30–40) |

GBP-LIBOR-3M | 27 | 22 | 17 | (10–17) |

GBP-LIBOR-6M | 33 | 28 | 24 | (18–32) |

Spreads in basis points. |

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Henrard, M.P.
LIBOR Fallback and Quantitative Finance. *Risks* **2019**, *7*, 88.
https://doi.org/10.3390/risks7030088

**AMA Style**

Henrard MP.
LIBOR Fallback and Quantitative Finance. *Risks*. 2019; 7(3):88.
https://doi.org/10.3390/risks7030088

**Chicago/Turabian Style**

Henrard, Marc Pierre.
2019. "LIBOR Fallback and Quantitative Finance" *Risks* 7, no. 3: 88.
https://doi.org/10.3390/risks7030088