Bond with options

The values of the put and call options decrease when interest rate volatility decreases, so the value of the callable bond will increase and the value of the putable bond will decrease.

Given that the value of a callable bond = option free bond value - call option value and the value of a putable bond = option free bond value + put option value isnt the above comment wrong ? surely when interest rate volatilty decreases the price of the callable bond will decrease more than the price of the putable ?

I believe the statement you listed is actually correct. My understanding is that the value of the callable bond will have an inverse relation to interest rate volatility and the value of the putable bond will have a direct relation. So by that logic, your statement,

" surely when interest rate volatilty decreases the price of the callable bond will decrease more than the price of the putable"

is off because when volatility decreases, the value (and seemingly subsequent price) of the callable should increase, not decrease. I’ve summarized below:

Callable Bonds

When volatility goes up, call value goes up, and the callable bond value goes down (Callable bond value = straight value - call value)

When volatiity goes down, call value goes down, and the callable bond value goes up

Putable Bonds

When volatility goes up, put value goes up, and the putable bond value goes up

When volatility goes down, put value goes down, and the putable bond value goes down

Put simply, decreased (increased) volatility is good (bad) for callable bonds and bad (good) for putable bond values.

Yes - that makes perfect sense. thanks