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September 2022 Q6

H

Hashini Wickramasuriya

Made first post
Looking for an explanation for q6,(I),(a). Don't understand by what's meant by "A 1 year zero coupon bond will be issued at time 3 and has a theoriatical price of 95$ per $100, and how the answer follows this.
 
Hi Hashini,

This means a bond is issued at time 3 for $95 and redeemed at time 4 for $100. From this information, we can work out the 1-year forward rate that applies from time 3 to be the rate that discounts the $100 for 1 year to become $95.

Once we have the 1-year forward rate from time 3, we can use the relationship between spot and forward rates to work out the 3-year spot rate. This is set out in section 1.2 of chapter 11 of the CMP, including a useful diagram towards the bottom of that page. Essentially, a 4-year accumulation factor (to go from time 0 to time 4 using the 4-year spot rate) will be the same as a 3-year accumulation factor (to go from time 0 to 3 using the 3-year spot rate) multiplied by a 1-year accumulation factor (to go from time 3 to time 4 using the 1-year forward rate derived according to the paragraph above).

Thanks,
Richie
 
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