Quote:
Originally Posted by Handynasty
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.

I’m very surprised the book says that. What about the coupon due in 3 years? Is it discounted by 1/(1.02^6)?
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.