Volatility risk only applies in the case of a called bond, as in the case of call risk. Volatility in bonds (i.e. the extent of price/rate changes around the mean in the past) and expected volatility is one of the major inputs in the price of an option. Thus, the rate/price of a call bond will change as volatility and expected volatility change. In general:
Price of a call bond = price of option-free bond – price of the embedded call option.
The higher volatility is the higher is the value of the call option. The reverse also holds, i.e. in the case of putable bonds:
Price of the put bond = price of option-free bond + price of the embedded put option.