Copyright © 2021 ARC, All rights reserved

1. Yield Curve Building using a mixture of instruments

We're going to construct in detail a zero-coupon yield curve, called zero curve as well, with Euribors, FRAs, Swaps by using bootstrapping method. First let's recall that the bootstrapping method is a process of obtaining the zero rate at a particular maturity using the zero rate from the previous maturity.

2. Instruments description

suppose we get from financial markets the quotations of the following instruments. The trade date is 2021-05-06.

2.1. Deposits

	instrument code	rate
0	Eonia	0.0030
1	Euribor1M	0.0031
2	Euribor2M	0.0032
3	Euribor3M	0.0033
4	Euribor6M	0.0034
5	Euribor9M	0.0035
6	Euribor1Y	0.0036

2.2. FRAs

	day count convention	months to start	months to end	rate
0	Actual360	12	15	0.0040
1	Actual360	13	16	0.0041
2	Actual360	14	17	0.0042
3	Actual360	17	20	0.0043
4	Actual360	20	23	0.0044

2.3. Swap rates

	maturity	interest periodicity	coupon rate	fixed_leg.day_count_convention	floating_leg.index_name
0	2Y	6M	0.0050	Actual360	Euribor6M
1	2Y6M	6M	0.0051	Actual360	Euribor6M
2	3Y	6M	0.0052	Actual360	Euribor6M
3	4Y	6M	0.0053	Actual360	Euribor6M
4	5Y	6M	0.0054	Actual360	Euribor6M
5	6Y	6M	0.0055	Actual360	Euribor6M
6	7Y	6M	0.0056	Actual360	Euribor6M
7	8Y	6M	0.0057	Actual360	Euribor6M
8	9Y	6M	0.0058	Actual360	Euribor6M
9	10Y	6M	0.0059	Actual360	Euribor6M

3. Bootstrapping of spot rates

The input market data are a mixture of instruments: Deposits, FRAs and Swaps. We have already computed zero rates from deposits, FRAs and Swaps by using bootstrapping method. For more details, you could look into the following test scenarios:

1. Yield curve construction with Eonia and Euribor
2. Yield curve construction with Forward Rate Agreements
3. Yield curve construction with swaps

Just keep in mind that the short end of the zero curve, out to 1year, is derived using ON (Overnight), 1M, 2M, until 1Y interbank deposit rates quoted in the market. The FRAs are used to build the middle of the zero curve. The long end of the swap curve out to ten years is derived directly from observable coupon swap rates.

4. The zero curve constructed

The following table contains the computed zero-coupons by maturity with Actual/360 day count convention and Continuous compounding.

	maturity date	zero coupon
0	2021-05-07	0.003000
1	2021-06-10	0.003089
2	2021-07-12	0.003188
3	2021-08-10	0.003286
4	2021-11-10	0.003389
5	2022-02-10	0.003488
6	2022-05-10	0.003587
7	2022-08-10	0.003669
8	2022-09-12	0.003707
9	2022-10-11	0.003740
10	2023-01-10	0.003823
11	2023-04-11	0.003897
12	2023-05-10	0.004988
13	2023-11-10	0.005089
14	2024-05-10	0.005190
15	2025-05-12	0.005284
16	2026-05-11	0.005389
17	2027-05-10	0.005493
18	2028-05-10	0.005594
19	2029-05-10	0.005696
20	2030-05-10	0.005798
21	2031-05-12	0.005896

<AxesSubplot:xlabel='maturity date'>