Expected volatility is a major factor that affects the value of an option. Expected volatility of an option on bond is referred to as 'expected yield volatility'. The value of an option is directly related to the expected yield volatility. In other words, greater the expected yield volatility, greater would be the value of the option. Let us see how this works for a callable bond.
The price of a callable bond can be determined as follows:
Price of callable bond = Price of option-free bond - Price of embedded call option
Let us assume that all other factors except expected yield volatility are constant. Now if the expected yield volatility increases the price of the call option will also increase. Hence, the price of the callable bond would decrease.
In case of a putable bond, the price can be decomposed into the following two elements:
Price of putable bond = Price of option-free bond + Price of embedded option
A decrease in expected yield volatility would result in a decline in the price of the embedded put option. Therefore, the price of a putable bond would also decrease.
Volatility risk can be defined as the risk that the price of a bond with an embedded option will decrease when expected yield volatility changes.