Fixed Income Securities, 4th Edition

APPENDIX TO CHAPTER 13Interest Rate Swaps

A13.1 PRICING A EURIBOR SWAP AS OF FEBRUARY 24, 2022

This section prices a two‐year fixed‐for‐floating swap, where the floating rate is three‐month Euribor. The inputs are the term structure of €STR OIS given in Table A13.1, the two‐year Euribor swap rate of 0.078%, and the two‐year €STR–Euribor basis swap spread of 0.138%. All cash flows are assumed to follow the actual/360 convention, and all of the relevant dates are assumed to be business days.

The OIS rates in the fourth column of the table are observed in the market. The discount factors are calculated by setting the present value of the fixed payments on each OIS (including the fictional notional amount at maturity) equal to par, which is the value of the floating legs that pay compounded daily €STR. Letting denote the discount factor for years, the equations determining the discount factors, along the same lines as for SOFR swaps explained in Chapter 2, are the following,

TABLE A13.1 €STR OIS Rates as of February 24, 2022.

Term	Term	Term	Rate	Discount	Fwd Rate
(years)	(date)	(days)	(%)	Factor	(%)
0.25	05/24/2022	89	−0.5695	1.0014099	−0.1408
0.50	08/24/2022	181	−0.5580	1.0028134	−0.1400
0.75	11/24/2022	273	−0.5110	1.0038902	−0.1073
1.00	02/24/2023	365	−0.4380 ...