Can't understand how forward rate formula was derived

[rvstrien]

Hi all,

In my finance book about derivatives (hull, 8th edition), on page 85, the following formula is presented for calculating forward rates:

Rf = (R2*T2 - R1*T1) / T2 - T1

The book states that it can also be written as:

Rf = R2 + (R2 - R1) * (T1 / (T2 - T1))

I can't seem to understand how this derivation was made. Any tips (please do provide the intermediate steps)?

Many thanks in advance,
Remco.

 

[Deleted member 4993]

Hi all,

In my finance book about derivatives (hull, 8th edition), on page 85, the following formula is presented for calculating forward rates:

Rf = (R2*T2 - R1*T1) / T2 - T1

The book states that it can also be written as:

Rf = R2 + (R2 - R1) * (T1 / (T2 - T1))

I can't seem to understand how this derivation was made. Any tips (please do provide the intermediate steps)?

Many thanks in advance,
Remco.

That is supposed to be:

\(\displaystyle R_f \ = \ \dfrac{R_2 * T_2 - R_1*T_1}{T_2} \ - \ T_1\)

or is it supposed to be:

\(\displaystyle R_f \ = \ \dfrac{R_2 * T_2 - R_1*T_1}{T_2 \ - \ T_1}\)

 

[rvstrien]

That is supposed to be:

\(\displaystyle R_f \ = \ \dfrac{R_2 * T_2 - R_1*T_1}{T_2} \ - \ T_1\)

or is it supposed to be:

\(\displaystyle R_f \ = \ \dfrac{R_2 * T_2 - R_1*T_1}{T_2 \ - \ T_1}\)

Its last equasion you posted, where T1 is in the denominator of the fraction.

 

[Deleted member 4993]

\(\displaystyle R_f \ = \ \dfrac{R_2 * T_2 - R_1*T_1}{T_2 \ - \ T_1}\)

\(\displaystyle R_f \ = \ \dfrac{R_2 * T_2 \ - \ R_1*T_1 \ - \ R_2*T_1 \ + \ R_2*T_1}{T_2 \ - \ T_1}\)

\(\displaystyle R_f \ = \ \dfrac{R_2 * T_2 \ - \ R_2*T_1 \ + \ R_2*T_1 \ - \ R_1*T_1 }{T_2 \ - \ T_1}\)

\(\displaystyle R_f \ = \ \dfrac{R_2 * (T_2 \ - \ T_1) +\ (R_2 \ - \ R_1)*T_1}{T_2 \ - \ T_1}\)

\(\displaystyle R_f \ = \ R_2 \ + \ (R_2 \ - \ R_1) * \dfrac{T_1}{T_2 \ - \ T_1}\)

Simple algebra !!!!

 

[rvstrien]

Thanks a lot for this Subhotosh! I really helped me a lot.

You are pbbly right that it's simple algebra. Will poat in the other forum next time.

Thanks again!

cheers!