L1.T4.Basic Bond Pricing (spot and forward rates)
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HI skoh, see here http://forum.bionicturtle.com/threads/shortcut-to-forward-rates-if-you-have-bond-prices.4927/
... this technique is not actually found directly in any assignment, to my knowledge, but GARP does like to quiz it
... this technique is not actually found directly in any assignment, to my knowledge, but GARP does like to quiz it
Hi David,
I have a question on L1.T4 Basic bond pricing Question 13.5:
I tried to find the answer using the well known relationship:
[1+z(1)/2]^2 = [1+z(0.5)/2]*[1+r(0.5,1)/2]
where z is the zero spot rate and r the forward rate.
Works pretty well for the first two CFs. However, solving for z(2) gives me 4.56% (consistent with your answer), so I thought discounting the 103 at (1+0.0456/2)^-3 would give me the PV (semi-annual coupon). But the solution says using 1.0456.
In my view this is inconsistent with the answer in question 12.5 which asks to discount using directly the zero spot rates (also semi-annual coupon). Could you help me on that?
Many thanks.
Chris
I have a question on L1.T4 Basic bond pricing Question 13.5:
I tried to find the answer using the well known relationship:
[1+z(1)/2]^2 = [1+z(0.5)/2]*[1+r(0.5,1)/2]
where z is the zero spot rate and r the forward rate.
Works pretty well for the first two CFs. However, solving for z(2) gives me 4.56% (consistent with your answer), so I thought discounting the 103 at (1+0.0456/2)^-3 would give me the PV (semi-annual coupon). But the solution says using 1.0456.
In my view this is inconsistent with the answer in question 12.5 which asks to discount using directly the zero spot rates (also semi-annual coupon). Could you help me on that?
Many thanks.
Chris
Hi Chris,
I agree with your general approach, if we extend to z(1.5):
[1+z(1.5)/2]^(1.5*2) = [1+f(0.5)/2]*[1+f(0.5,1)/2]*[1+f(1,1.5)/2], such that
[1+z(1.5)/2] = ([1+f(0.5)/2]*[1+f(0.5,1)/2]*[1+f(1,1.5)/2])^(1/3)
z(1.5) = [([1+f(0.5)/2]*[1+f(0.5,1)/2]*[1+f(1,1.5)/2])^(1/3) - 1] * 2. In this case:
z(1.5) = [([1+1%/2]*[1+3%/2]*[1+5%/2])^(1/3) - 1] * 2 = 2.99%. I hope that helps,
I agree with your general approach, if we extend to z(1.5):
[1+z(1.5)/2]^(1.5*2) = [1+f(0.5)/2]*[1+f(0.5,1)/2]*[1+f(1,1.5)/2], such that
[1+z(1.5)/2] = ([1+f(0.5)/2]*[1+f(0.5,1)/2]*[1+f(1,1.5)/2])^(1/3)
z(1.5) = [([1+f(0.5)/2]*[1+f(0.5,1)/2]*[1+f(1,1.5)/2])^(1/3) - 1] * 2. In this case:
z(1.5) = [([1+1%/2]*[1+3%/2]*[1+5%/2])^(1/3) - 1] * 2 = 2.99%. I hope that helps,
Hi Bryon,
You are not wrong to assume annual in 13.5 because the question does not explicitly say price the bond "with semi-annual compounding." By convention (connotation), the reason to use semi-annual is simply that the coupons pay semi-annually; e.g., if the coupons pay annual, then (in my opinion), annual discounting would be the appropriate (by convention) assumption if none is explicitly given. My question 13.5 is technically imprecise for not explicitly stating, but it's borderline: many questions let the compound frequency follow the coupon frequency (however, as Hull assumes continuous, he obviously never does this!)
The actual *reason* the question assumes semi-annual is: the source is Tuckman, and Tuckman assumes semi-annual coupon bonds with semi-annual discounting throughout his text.
Exam-wise, this is an issue we have carefully expressed to GARP over the last few years and I'm confident the assumption will be explicitly stated; e.g., on the last exam, I'm told the instructions were to assume annual (as you did) unless otherwise told. Thanks,
You are not wrong to assume annual in 13.5 because the question does not explicitly say price the bond "with semi-annual compounding." By convention (connotation), the reason to use semi-annual is simply that the coupons pay semi-annually; e.g., if the coupons pay annual, then (in my opinion), annual discounting would be the appropriate (by convention) assumption if none is explicitly given. My question 13.5 is technically imprecise for not explicitly stating, but it's borderline: many questions let the compound frequency follow the coupon frequency (however, as Hull assumes continuous, he obviously never does this!)
The actual *reason* the question assumes semi-annual is: the source is Tuckman, and Tuckman assumes semi-annual coupon bonds with semi-annual discounting throughout his text.
Exam-wise, this is an issue we have carefully expressed to GARP over the last few years and I'm confident the assumption will be explicitly stated; e.g., on the last exam, I'm told the instructions were to assume annual (as you did) unless otherwise told. Thanks,
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