Question

“Suppose that 3-month, 6-month, 12-month, 2-year and 3-year OIS rate are 2.0%, 2.5%, 3.2%, 4.5%, and 5%, respectively. The 3-month, 6-month, and 12-month OISs involve a single exchange at maturity; the 2-year and 3-year OIS involve quarterly exchanges. The compounding frequencies used for expressing the rates correspond to the frequency of exchanges. Calculate the OIS zero rates using continuous compounding. Interpolate between continuously compounded rates linear to determine rates between 6 months and 12 months, between 12 months and 2 years and between 2 years and 3 years.

Answer 1

Solution:

The two-year and three-year OIS rates are the yields on par yield bonds. The zero rates are as follows:

3-month = ln(1 + R)

                = ln(1 + 0.02)

= 1.9803%

6-month = ln(1 + 0.025)

= 2.469%

12-month = ln (1 + 0.032)

    = 3.1499%

2-year = 4ln(1 + R/4)

            = 4ln(1 + 0.045/4)

            = 4.4749%

3-year = 4ln(1 + 0.05/4)

            = 4.9690%