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I am preparing for FRM level 2, but I ran into a question whose answer was confusing to me:

Q

In the answer, it says "all other things remaining the same, the higher the call price, the higher the price of a callable bond." I thought a higher call price is benefit to the seller and harmful to the investor, why does a higher call price lead to a higher callable bond price? Is it because for a callable bond with a higher call price, the seller will have to pay more to the investors, therefore the price of the callable bond with a high call price is higher?

Please correct me my understanding is not correct, thank you so much!

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    $\begingroup$ I may be wrong but as they say all things remaining the same, it means that the strike price is not moving. Therefore, a higher call price means the call is deeper in the money, meaning the price of the bond is higher too $\endgroup$ – Mayeul sgc Nov 8 '19 at 9:28
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A callable bond is a little like a put. Companies issue them to protect against a drop in interest rates, and with a higher call price, interest rates need to drop even further to be called.

In essence, in the same way a put with a lower strike is more desirable to a buyer, a callable bond with higher call value will be priced higher than otherwise equivalent bonds.

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To the investor, a callable bond can be seen a ordinary bond plus a short position in a call. If the strike price is higher, the call has less value, and the "package" ordinary bond minus call has more value.

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    $\begingroup$ A mental shortcut to help see the logic: if the call price was a very big number M, then the bond would essentially be non-callable, and such a bond is more desirable from an investor's point of view -> higher price. $\endgroup$ – Alex C Nov 8 '19 at 18:27

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