Volatility risk involves bonds with embedded options. Expected volatility or "vol" effects the option price within a callable or puttable bond. Greater expected yield vol yields a greater increase in the value of the option Callable bonds- Let's look at the components of a callable bond:
Price of Callable Bond = Price of option-free bond - Price of Embedded option.
As volatility increases, with all other factors holding the same, the price of the option will increase. This decreases the price of the bond.
The risk here is that volatility increases
Puttable bonds- Let's looks at the components of a puttable bonds.
Price of a Puttable Bond = Price of option-free bond + Price of embedded option
As volatility decreases with all other factors holding the same, the price of the option will decrease, which depresses the price of the bond.