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Financial Mathematics Old FM Forum 

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#3




Hi Gandalf,
It's from section 6.6 of the Financial Mathematics for Actuaries book by Chan, WaiSum, and Tse, YiuKuen. It's not approximation because a formula is given for semiannual coupon bond pricing using spot rates. And it seems to be the convention that spot rate is divided by 2 to get the semiannual spot rate. An example it gives is spot rate for payment due in three years is 4%, so coupon at 2.5 year is discounted by 1/(1.02^5). I'm wondering if that's always the convention. And on the exam, would the question specify the way to use spot rates for semiannual payments. 
#4




The convention in financial markets is to quote bond equivalent yield, i.e. nominal semiannual rate. Dividing the annual rate by 2 matches up with that.
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#5




Quote:
To my way of thinking, the entire premise of spot rates is that you can value a payment due in k years using the price of a zerocoupon bond maturing in k years. To value a payment due in k.5 years, you would look at the price of a zerocoupon bond maturing in k.5 years, not one maturing in k years. (If the only information available was the price of one maturing in k years, you might base the value on that, but it would be an estimate / approximation.) As to what you would see on the exam, I don´t know. I would hope they wouldn’t throw such a curve ball at you. If they do, hope that the answers aren’t so close together that it matters whether you use 1.02^5 or 1.04^2.5. Good luck. 
#6




If you have semiannual payments, there would generally be a separate spot rate for each half year quoted on a nominal annual basis. The payment six months from now would have a discount factor (1 + s1/2) while the payment one year from now would be discounted at (1+ s2/2)^2. .

#7




Quote:
Looking at the FM sample questions, specifically 33 and 34, you are given annual spot rates and you treat them as annual effective rates, not annual rates convertible semiannually. 
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financial mathematics, spot rate 
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