Six nonth semi annual forward rate

[Angelinelyt]

Hi david,

I read on your study notes in the financial markets and products on hull regarding interest rates, page 53 whereby we are asked to calculate the six month semi annial forward rate starting in 1.5 years.
Please can you explain how the calculation formula?
Many thanks!

 

[Angelinelyt]

Calculation table as follows

 

[David Harper CFA FRM]

Hi @Angelinelyt (thank you for trying to give the thread a prefix, "FAQ before the exam", but that prefix intends to refer to questions that a potential FRM candidate might have about the FRM designation before they commit to the exam)

With respect to this forward calculation, please see here for in depth discussion https://forum.bionicturtle.com/threads/six-nonth-semi-annual-forward-rate.9900/
... so the solution follows from the no-arbitrage relationship:
(1 + 2.25%/2)^(1.5*2) * (1 + f/2) = (1 + 2.50%/2)^(2.0*2), I asusme you can solve for the forward rate, f,

The general form, under semi-annual compounding is given by:
(1 + s1/2)^(t1*2) * (1 + f/2)^([t2-t1]*2) = (1 + s2/2)^(t2*2); i.e., the spot rate return, s1 over time t1, rolled over into the forward rate, f over time [t2-t1], should equal the return over spot rate, s2 over t2. I hope that explains!

 

[boom]

Hi @Angelinelyt (thank you for trying to give the thread a prefix, "FAQ before the exam", but that prefix intends to refer to questions that a potential FRM candidate might have about the FRM designation before they commit to the exam)

With respect to this forward calculation, please see here for in depth discussion https://forum.bionicturtle.com/threads/six-nonth-semi-annual-forward-rate.9900/
... so the solution follows from the no-arbitrage relationship:
(1 + 2.25%/2)^(1.5*2) * (1 + f/2) = (1 + 2.50%/2)^(2.0*2), I asusme you can solve for the forward rate, f,

The general form, under semi-annual compounding is given by:
(1 + s1/2)^(t1*2) * (1 + f/2)^([t1-t2]*2) = (1 + s2/2)^(t2*2); i.e., the spot rate return, s1 over time t1, rolled over into the forward rate, f over time [t2-t1], should equal the return over spot rate, s2 over t2. I hope that explains!

Shouldn't it be (...) (1 + f/2)^([t2-t1]*2) (...) ?

Regards,

 

[David Harper CFA FRM]

HI @boom Yes, indeed, thank you. Fixed above. I love it when people care about the details