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Hi,
q27 from Kaplan asks for 5 months forward rate basing on 3 months and 1 year forwards (1,9066 and 1,8901). The calculation goes as follows: 1,9066*(7/9) + 1,8901*(2/9) = 1,9029
Can someone explain where these proportions – 7/9 and 2/9 – come from?Hi, I’ll try to explain:
Suppose the forward rate is f(t), where t month number.
For example f(3) = 1,9066, f(12) = 1,8901. Then we reasonably assume that between forward rate and time a linear dependence F(t) exists (that is called linear interpolation):
F(t) = f(3)+(f(12)-f(3))/(12-3)*(t-3) – linear dependence equation (note that F(3)=f(3) and F(12)=f(12)!). After excercise with fractions you get this:
F(t)=f(3)*(12-t)/(12-3)+f(12)*(t-3)/(12-3), then find F(5)
F(5)=f(3)*(12-5)/(12-3)+f(12)*(5-3)/(12-3)=
=1,9066*(7/9) + 1,8901*(2/9) = 1,9029
The same idea lies behind the IRR interpolation formula. See also https://en.wikipedia.org/wiki/Linear_interpolation .
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