Does a lower interest rate volatility imply falling interest rates?
No.
Rates might be at 20% and stable.
Ick.
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My Kaplan Quicksheet says, “When interest rate volatility increases: Value of call option increases, Value of Put Option increases, Value of callable bond decreases, Value of Putable bond increases.”
Optionality to a call or a put increases in value, but wouldn’t the value of a putable bond decrease too?
Is Kaplan viewing their opinions solely through the eyes of the bond holder and not the issuer?
Since the value of the putable bond = value of straight bond + value of put, the value of the putable bond will increase as the value of the put increases. I tend to have to write out these relationships several times until they really start to click.
Why does the value of a putable bond increase while the value of a callable bond decreases when interest rate volatility increases?
Could it not be the reverse with an increase in interest rate volatility? I just envision rates going from 8% down to 7%, up to 9%, etc. etc.
If rates are going to bounce around and I’m an issuer, not a holder of a callable bond, I would view that call provision as valuable.
I remember back in the 80s when people were getting mortgages @ 20% and higher!!! 
So does the term “interest rate volatility” only apply to upward movements and not downward?
Um . . . no.
Standard deviation of continuously compounded returns. Ups and downs.
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Okay, that makes perfect sense. Now, why does the value of a putable bond increase while the value of a callable bond decreases when interest rate volatility increases?
If rates are going to bounce around and I’m an issuer, not a holder of a callable bond, I would view that call provision as valuable. I would call the bonds when rates move lower during the said “volatility”.
My Kaplan Quicksheet says, “When interest rate volatility increases: Value of call option increases, Value of Put Option increases, Value of callable bond decreases, Value of Putable bond increases.”
There is very simple explanation
Value of Puttable Bond = Value of Simple Bond PLUS Value of Embedded Put Option
Value of Callable Bond = Value of Simple Bond MINUS Value of Embedded Call Option
When interest rate volatility increases the value of both options increases too. Value of Callable Bond decreases then.
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Increase in vol , increases value of long option
If you owna putable bond you have
Bought a bond and are LONG a put option
if you own a callable bind you have
Bought a bond and are SHORT a call option
You have to take the perspective of the investor, not the issuer.
Owning a callable bond in a volatile scenario increases the chances of it being called away from me, so it’s worth less. Conversely, owning a putable bond gives me the optionality to put it back to the issuer, making it worth more for me.