Pricing of Forward Rate Agreements
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![Page 1: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/1.jpg)
Pricing of Forward Rate Agreements
ANALYTICAL FINANCE II
MICHAEL AUSSIEKER, OLIVER GRACE
![Page 2: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/2.jpg)
Step One
Calculate the discount factors:
![Page 3: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/3.jpg)
Step Two
Calculate the Zero Coupon Rates:
![Page 4: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/4.jpg)
The Nelson–Siegel–Svensson model
where are parameters calculated via least squares or a solver such as the one found in Microsoft Excel.
![Page 5: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/5.jpg)
Calculate Parameters
Used R language to calculate parameters below:
Parameters β0 β1 β2 β3 τ1 τ2
3 month Forward Rate 1.861033 -1.707564 -6.009837 8.069004 3.908024 6.417405
6 month Forward Rate -0.6770534 0.7609579 1.115105 10.88655 0.5622814 12.64441
OIS Forward Rate -1.349865 1.470678 -1.418929 12.62976 1.119861 6.417405
OIS Zero Rate 1.914176 -1.813437 -4.888361 5.597794 3.350408 6.417405
![Page 6: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/6.jpg)
Step Three
Calculate Zero Rate Curve for EUR 3M, EUR 6M, EUR OIS 3M, EUR OIS 6M with NSS
Find 3x6 etc Forward Rates from EUR 3M and 3x9 etc Rates from EUR 6M
Do same for EUR OIS 3M and EUR OIS 6M curves
![Page 7: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/7.jpg)
3 Month FRA
2013
-11-
01
2015
-01-
01
2016
-03-
01
2017
-05-
01
2018
-07-
01
2019
-09-
01
2020
-11-
01
2022
-01-
01
2023
-03-
01
2024
-05-
01
2025
-07-
01
2026
-09-
01
2027
-11-
01
2029
-01-
01
2030
-03-
01
2031
-05-
01
2032
-07-
01
2033
-09-
01
2034
-11-
01
2036
-01-
01
2037
-03-
01
2038
-05-
01
2039
-07-
01
2040
-09-
01
2041
-11-
01
2043
-01-
010.0000000
0.5000000
1.0000000
1.5000000
2.0000000
2.5000000
3.0000000
3.5000000
4.0000000
Zero Rate Curve via NSS3MOT Forward
![Page 8: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/8.jpg)
6 Month FRA
2014
-02-
01
2015
-03-
01
2016
-04-
01
2017
-05-
01
2018
-06-
01
2019
-07-
01
2020
-08-
01
2021
-09-
01
2022
-10-
01
2023
-11-
01
2024
-12-
01
2026
-01-
01
2027
-02-
01
2028
-03-
01
2029
-04-
01
2030
-05-
01
2031
-06-
01
2032
-07-
01
2033
-08-
01
2034
-09-
01
2035
-10-
01
2036
-11-
01
2037
-12-
01
2039
-01-
01
2040
-02-
01
2041
-03-
01
2042
-04-
01
2043
-05-
01 -
0.500000
1.000000
1.500000
2.000000
2.500000
3.000000
3.500000
4.000000
NSS 3MOT Zero Rate6mo FRA
![Page 9: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/9.jpg)
2013
-11-
01
2014
-11-
01
2015
-11-
01
2016
-11-
01
2017
-11-
01
2018
-11-
01
2019
-11-
01
2020
-11-
01
2021
-11-
01
2022
-11-
01
2023
-11-
01
2024
-11-
01
2025
-11-
01
2026
-11-
01
2027
-11-
01
2028
-11-
01
2029
-11-
01
2030
-11-
01
2031
-11-
01
2032
-11-
01
2033
-11-
01
2034
-11-
01
2035
-11-
01
2036
-11-
01
2037
-11-
01
2038
-11-
01
2039
-11-
01
2040
-11-
01
2041
-11-
01
2042
-11-
010
0.5
1
1.5
2
2.5
3
NSS-3moZeorNSS-3moFor
![Page 10: Pricing of Forward Rate Agreements](https://reader036.fdocuments.in/reader036/viewer/2022072013/56812a73550346895d8df775/html5/thumbnails/10.jpg)
2014
-02-
01
2015
-02-
01
2016
-02-
01
2017
-02-
01
2018
-02-
01
2019
-02-
01
2020
-02-
01
2021
-02-
01
2022
-02-
01
2023
-02-
01
2024
-02-
01
2025
-02-
01
2026
-02-
01
2027
-02-
01
2028
-02-
01
2029
-02-
01
2030
-02-
01
2031
-02-
01
2032
-02-
01
2033
-02-
01
2034
-02-
01
2035
-02-
01
2036
-02-
01
2037
-02-
01
2038
-02-
01
2039
-02-
01
2040
-02-
01
2041
-02-
01
2042
-02-
01
2043
-02-
01 -
0.500000
1.000000
1.500000
2.000000
2.500000
3.000000
NSS-6moZeorNSS-6moFor