volatility risk on bonds

in an explanation of a question on exam 1 evening it says that only bonds with options have volatility risk. huh? prices of bonds go up and down. thus volatility risk. where am i going wrong?

The plan bond has the “interest rate risk” while volatility in option is considered the movement of the underlying of the call or put option…which in this case is the interest rate… I guess is more technical terminology…

no vol risk for straight bonds

The volatility risk on bonds with embedded options basically say that a more volatile bond will have a higer chance of having the option exercised. Thus, if you purchase a bond with a call option and the market rates cause the price of the bond to be very volatile, there is a greater chance that the company that issued the bond will call it when rates are down. Bad for the purchaser of the bond, good for the issuer. Same with put options, but this would be good for the purchaser and bad for the issuer. Just like stock options, the more volatile the underlying security, the more valuable the option. The risk depends on if you are long or short the option.