Good morning, Next week I'll have Derivates Final test and I've a doubt about Bond Option.

If I have one ZCB, price 90 with 3 month maturity and strike 100, and I want a minimum yield of 2%, what type of option I have to buy?

Is it correct think that if I've a ZCB and I want to make a floor for yield I've to buy a CALL Option?

How can I find option strike?

If I also have this table

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How can I get the option price using B&S model? Which is the numeraire I've to choose (bond price = 90 or 0,9 because the value of bond at maturity is 100 and today I have 90/100)?

  • 1
    $\begingroup$ A 3month ZCB with a price of 90 is very unlikely. Are you sure ? $\endgroup$
    – dm63
    Nov 25, 2022 at 11:31
  • $\begingroup$ I know it's quite strange, but the exercise is this one, I think it's only for didactic purpose $\endgroup$ Nov 25, 2022 at 11:54
  • $\begingroup$ Maybe it's denominated in one of those emerging markets exotic currencies with very high interest rate. :) $\endgroup$ Nov 25, 2022 at 20:26

1 Answer 1


The question doesn’t make much sense. A 2pct yield strike on a 3month ZCB is equivalent to roughly a 99.5 price strike. So you sell a 99.5 call for 30 days to cap the upside on your bond in case the yield drops below 2pct. But the strike is not in your table. And if the yield were really 40pct, that option would be worthless

  • $\begingroup$ Ok, it is a University Exercise so it isn't real. I want to put a floor and I have to find the strike. is it correct calculate (100-90)/100)*0,25 in order to find the yield and after that calculate the price with 2% yield? $\endgroup$ Nov 26, 2022 at 10:05
  • $\begingroup$ Yield = (100 - price)/0.25 approximately $\endgroup$
    – dm63
    Nov 26, 2022 at 11:51

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