Pricing of Forward Rate Agreements

ANALYTICAL FINANCE II

MICHAEL AUSSIEKER, OLIVER GRACE

Step One

Calculate the discount factors:

Step Two

Calculate the Zero Coupon Rates:

The Nelson–Siegel–Svensson model

where are parameters calculated via least squares or a solver such as the one found in Microsoft Excel.

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

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

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

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

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

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