Simple callable bond question question, option, price

wilslm

If the yield rises, will the price of a callable bond fall more or less than the price an option free bond?

Analyze_This

I would say less but I’m not 100% sure. If you think about it, as yields increase, there is less and less of a chance of a callable bond being called. (Why would a company call a bond during a period of high yields, when they’d have to issue new bonds at these higher yields?)

Andreas42

I said less on this one. Since the bond won’t trade above the call price, changing YTM at low yields will have practically no effect on the price.

LPoulin133

It will fall less. The price of the option also decreases, making the callable bond fall less.
Same thing for a putable bond–it doesn’t increase/decrease as much as option free bonds for given decreases/increases in yields.

bleach

If yield increases the price of the call becomes worthless (basically becomes an OTM call option)…so the price should move more or less with the option free…and moreso as the yield increases to infinity…

dotamasta

I kinda agree with you guys but im still confused. If you’re saying that the callable will fall less, that means at very high yields, the price of a callable bond is higher than the price of an option free (it has fallen less).
but look at this formula: callable = option free  option cost
as you can see the callable price will always be smaller than the option free (or equal to it, if option cost is zero). so is callable is smaller, how does it make sense that callable does not fall as much and remains higher than option free at high yeilds?

noel

Even at relatively high yields the option still has value to the issuer. Rates could still decrease at some point and it could end up being called.

Bad5shah

so in conclusion
when yields rise, callable bond will not fall as much as option free bond
when yeilds fall, putable bond will not rise as much as option free bond
correct?

joehogue

i think you have to look at this question from the point of view of moves to 0 and infinity….as the yield increases to infinity, the callable bond and the option free will act similiarly…when the yield decreases to 0, the putable bond will rise in tandem with the callable bond….as you approach 0 and infinity, respectively, the option values converge to zero.

jarobi04

and im sure that there is a proper answer…which looks at int rate volatility and values the put/call option more mathematically (like the BS does for equity options) than we need for this purpose…i think for now we can just keep it simple and view it as moves to either infinity or 0…