Can anybody please help me out with the below question with a brief explanation:-

A 10-year zero coupon bond is callable annually at par (its face value) starting at the beginning of year 6. Assume a flat yield curve of 10%. What is the bond duration? A- 10 Years B- 5 Years C- 7.5 Years D- Cannot be determined based on the data given.

According to me it should be 10 years as the duration of a zero coupon bond is always equal to its maturity. But I am not getting convinced with my answer because of the callable feature in the question. Can somebody please explain me in context of the callable feature on the zero coupon bond?

Thanks in advance!!

  • $\begingroup$ Think about it: What is the price of a zero coupon bond that can't be called? When would the issuer choose to call? What if rates are non-positive? $\endgroup$ – LocalVolatility Jan 11 '17 at 21:04
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    $\begingroup$ According to my knowledge, the issuer calls a coupon bond whenever he is getting a lower interest rate to finance its debt. But in zero coupon bond, there is no coupon and zero coupon bonds are always issued at discount. According to the question the yield is flat 10 %, so according to me there is no point in calling the bond. So now it becomes a normal zero coupon bond and hence its duration will be equal to its maturity. I can think only this far. Am i right? $\endgroup$ – Manish Jan 11 '17 at 22:56
  • $\begingroup$ I agree with you under the assumption that the rate curve is either constant or at least always positive for all maturities (which is I suppose what the question wants to imply). $\endgroup$ – LocalVolatility Jan 11 '17 at 23:39
  • $\begingroup$ Yes I also think the same. Well thanks LocalVolatility. $\endgroup$ – Manish Jan 13 '17 at 17:14

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