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 Financial Mathematics Old FM Forum

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#1
11-12-2017, 10:02 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128
Bonds question

I got this question right but the solution suggests my approach is really shaky.

So I know the coupon rate > interest rate which mean earliest redemption is the worst. Then I look towards the earliest redemption period, redemption = 1250. Then I set this up:

$1000=35a_{\overline{n|}2.5%}+1250v^{n}$

n=39.72 -> (D)40

How is it?
#2
11-12-2017, 10:24 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,256

Quote:
 Originally Posted by Futon I got this question right but the solution suggests my approach is really shaky. So I know the coupon rate > interest rate which mean earliest redemption is the worst. Then I look towards the earliest redemption period, redemption = 1250. Then I set this up: $1000=35a_{\overline{n|}2.5%}+1250v^{n}$ n=39.72 -> (D)40 How is it?
Earliest redemption is not necessarily worst (lowest value at the given yield) if the bond has a call premium. You have to calculate the value at the earliest call, and at each time the call premium steps down, which here would include the maturity date. You then take the lowest of the values. That price would give the assumed yield if call occurred at that date. Call on any other date would result in a higher realized yield.
#3
11-12-2017, 10:44 PM
 Futon Member SOA Join Date: Jul 2016 Studying for FM Posts: 128

Quote:
 Originally Posted by Academic Actuary Earliest redemption is not necessarily worst (lowest value at the given yield) if the bond has a call premium.
Thanks.

Quote:
 You have to calculate the value at the earliest call, and at each time the call premium steps down
What do you mean by step down?
#4
11-12-2017, 11:36 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,256

The call premium steps down from 250 to 125 after the 40th coupon and to 0 at the maturity date.

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