An interest rate swap is a financial derivative instrument in which two parties agree to exchange interest rate cash flows. It is used in order to hedge against or speculate on changes in interest rates.

In order to fix the future interest expenses relative to a debt (hedging of the interest rate risk), a corporate can enter into a swap: the debt is finally at fixed rate. However, if the interest rates decline, the corporate will not benefit from low rates.

Therefore, the net debt of corporate should be sufficiently fixed to secure interest expenses. However, the corporate can benefit from falling rates with a residual floating net debt.

As already mentioned, interest rate swaps can be used for speculation ends: if a bank anticipates a drop of rates, it can enter into a swap to pay floating rates and to receive fixed rates. As a consequence, if the interest rates really drop, the bank will pay less interest expenses (meanwhile, the bank will continue to receive the same fixed cash flows).

In an interest rate swap traded by two parties, each counterparty agreed to pay either a fixed or floating rate to the other counterparty. The swap has two legs: one is related to the cash flows paid by the counterparty A to the counterparty B ; the other is related to the cash flows paid by the counterparty B to the counterparty A. Characteristics of an interest rate swap are the following:

**Notional**: this notional amount is only used for calculating the size of cash flows to be exchanged. The notional amount is not exchanged if the 2 legs have the same currency

**Currency**: typically, currencies are the same for both legs (for instance: euro, dollar, etc.). By trading another financial derivative instrument, the Cross Currency Swap, 2 counterparties agreed to exchange cash flows in 2 different currencies.

**Trade date**: this is the date at which the swap is traded.

**Value date**: this is the date at which the swap is really effective, that is to say the date from which cash flows are calculated.

**End date**: this is the maturity date of the swap.

For each leg of a swap, the following characteristics are determined:

**Rate type**: fixed rate or floating rate. For example, the counterparty A pays a fixed rate to B (fixed leg) and B pays a floating rate to A (floating leg).

**Frequency**: this is the frequency at which cash flows are paid or received (often 3 months, 6 months or 1 year). The frequency of each leg can be different.

**Time basis**: this is the basis on which the cash flows calculation is based. For example, it can be 30/360: in this case, we consider that a year is equivalent to 360 days and a month is equivalent to 30 days.

The valuation of an interest rate swap is based not only on its characteristics (mentioned above), but also on market data (interest rates, foreign exchange rates, etc.). This is what we usually call "Mark-to-Market". At inception date, the rate of the fixed leg is generally determined in order to calculate a valuation equal to 0 at this date. If the valuation is not equal to 0, a cash payment will occur (the counterparty for which the valuation is positive will pay the other party).

To valuation an interest rate swap, several yield curves are used:

**The zero-coupon yield curve**, used to calculate the discount rates of future cash flows, paid or received, fixed or floating. Cash flows of each leg have to be discounted.

**The forward rate curve**, used to calculate the size of the floating cash flows paid (or received). If the rate of the floating leg is 6 month Libor, this curve will inform on the level of the 6 month Libor at each fixing date (we calculate therefore the size of the cash flows). This curve can be deducted from the zero-coupon yield curve, or collect directly on a data market provider (Bloomberg, Reuters, etc.).

Once cash flows calculated, we have to sum each discounted cash flow on each leg.

Finally, the swap valuation is the difference between the sum of the discounted received cash flows and the sum of the discounted paid cash flows.

- Trade date: December 31, 2014
- End date: December 31, 2019
- Valuation date: June 30, 2015
- Notional: 100 000 000 EUR
- Payment frequency: 6 months for the fixed leg and for the floating leg
- Fixed rate paid: 2%
- Floating rate received: Euribor 6 mois
- Basis: 30/360 (a month is equivalent to 30 days)

Please find below the market data on valuation date (June 30, 2015). Figures are the following:

**Discount rate**: used to discount the future cash flows**Distance from the valuation date**: used to calculate the discount factor**Discount factor**: future cash flows has to be multiplied by this factor to be discounted. It is equal to: 1/(1+Discount rate)^(Distance from the valuation date)**Rates of floating cash flows**(calculated from the forward rate curve): used to calculated the size of the floating cash flows

Date | Discount rate (zero-coupon curve) | Distance from June 30, 2015 (basis 30/360) | Discount factor | Rate of floating cash flows (forward rate curve) |
---|---|---|---|---|

31/12/2015 | 0,051 | 0,5 | 0,99975 | 0,05 |

30/06/2016 | 0,0734 | 1 | 0,99927 | 0,0954 |

30/12/2016 | 0,0968 | 1,5 | 0,99855 | 0,1437 |

30/06/2017 | 0,1224 | 2 | 0,99756 | 0,1992 |

29/12/2017 | 0,1629 | 2,4972 | 0,99594 | 0,3261 |

29/06/2018 | 0,2146 | 2,9972 | 0,9936 | 0,4721 |

31/12/2018 | 0,2753 | 3,5 | 0,99042 | 0,6358 |

28/06/2019 | 0,3406 | 3,9944 | 0,98651 | 0,7998 |

31/12/2019 | 0,4139 | 4,5 | 0,98158 | 0,9906 |

Please find below the calculation detail of the discounting of the future fixed cash flows (fixed leg):

Fixed leg (interest rate equals to 2%) | ||||||
---|---|---|---|---|---|---|

Coupon date | Interest rate (annual basis) | Cash flow | Notional cash flow | Sum of cash flows | Discount factor | Discounted cash flow |

31/12/2015 | 2% | -1 000 000 | -1 000 000 | 0,99975 | -999 745 | |

30/06/2016 | 2% | -1 000 000 | -1 000 000 | 0,99927 | -999 267 | |

30/12/2016 | 2% | -1 000 000 | -1 000 000 | 0,99855 | -998 550 | |

30/06/2017 | 2% | -1 000 000 | -1 000 000 | 0,99756 | -997 556 | |

29/12/2017 | 2% | -994 444 | -994 444 | 0,99594 | -990 411 | |

29/06/2018 | 2% | -1 000 000 | -1 000 000 | 0,9936 | -993 595 | |

31/12/2018 | 2% | -1 005 556 | -1 005 556 | 0,99042 | -995 926 | |

28/06/2019 | 2% | -988 889 | -988 889 | 0,98651 | -975 549 | |

31/12/2019 | 2% | -1 011 111 | -100 000 000 | -101 011 111 | 0,98158 | -99 150 952 |

Sum of cash flows | -107 101 551 |

The cash flows are calculated by multiplying the notional of the swap (100 million EUR) by the interest rate (2%) and by the coupon duration (about 0,5 in our example).

Please find below the calculation detail of the discounting of the future floating cash flows (floating leg):

Floating leg (interest rates calculted from the forward rate curve) | ||||||
---|---|---|---|---|---|---|

Coupon date | Interest rate = forward rate | Cash flow | Notional cash flow | Sum of cash flows | Discount factor | Discounted cash flow |

31/12/2015 | 0,05% | 25 000 | 25 000 | 0,99975 | 24 994 | |

30/06/2016 | 0,0954% | 47 700 | 47 700 | 0,99927 | 47 665 | |

30/12/2016 | 0,1437% | 71 850 | 71 850 | 0,99855 | 71 746 | |

30/06/2017 | 0,1992% | 99 600 | 99 600 | 0,99756 | 99 357 | |

29/12/2017 | 0,3261% | 162 144 | 162 144 | 0,99594 | 161 486 | |

29/06/2018 | 0,4721% | 236 050 | 236 050 | 0,9936 | 234 538 | |

31/12/2018 | 0,6358% | 319 666 | 319 666 | 0,99042 | 316 605 | |

28/06/2019 | 0,7998% | 395 457 | 395 457 | 0,98651 | 390 122 | |

31/12/2019 | 0,9906% | 500 803 | 100 000 000 | 100 500 803 | 98 650 042 | |

Sum of cash flows | 99 996 555 |

The valuation of the swap is the sum of the discounted (and signed) future cash flows of each leg. As of June 30, 2015, the interest rate swap valuation is negative: -7,1 million EUR.

Discounted cash flows | |
---|---|

Fixed leg (paid cash flows) | - 107 101 551 |

Floating leg (received cash flows) | 99 996 555 |

Swap valuation | - 7 104 996 |