Hedging a Bond’s Minimum Yield with a Bond Option

Summary

The document considers how to use an option on a zero-coupon bond to protect a minimum yield. Its response translates a yield threshold into an approximate bond-price strike, then explains the position direction: selling a call at that strike limits the bond’s upside if yields fall below the target. The example involves a bond priced below its maturity value and a stated yield threshold, but the response notes that the necessary strike is absent from the referenced table.

This illustrates the inverse relationship between bond prices and yields and how a price option can express a yield constraint. It does not provide enough market inputs to calculate an option premium with Black–Scholes, nor does it specify a full pricing setup or validate model suitability. The result is a brief conceptual correction to the question’s proposed call purchase, rather than a complete hedging or valuation procedure.

Key ideas

• A yield threshold on a zero-coupon bond can be translated into a corresponding bond-price strike.
• Bond prices rise when yields fall, so a call at the threshold price can cap upside from falling yields.
• The response recommends selling the call to limit gains when the yield drops below the target.
• An option premium cannot be calculated from the information provided because key inputs are missing.

Tags

# University problem about Bond option


# University problem about Bond option












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

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)?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/73877

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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.