The value (premium paid) of an option today depends on how likely it is that the price of the bond will be different from the exercise price, and by how much. Complex formulae have been devised but, intuitively, one can guess that the option price formula will include the current price of the bond, the exercise price, and its volatility (the standard deviation of the probability distribution of the value of the underlying bond). Indeed, when volatility is large, there is a greater chance of a large price movement and of a large profit.
Banks holding or writing options are facing a new type of risk: the value of their option portfolio may change when:
the price of bonds changes;
the volatility of bond prices changes. ...