Callable

Exam items lean on one identity: callable bond value = value of an otherwise-identical straight (option-free) bond − value of the embedded call option. The classic vignette gives you the straight-bond price and the call-option value and asks for the callable price, or flips it to back out the embedded option — recognize that the option is subtracted because it is held by the issuer. A second favorite: when interest-rate volatility rises, the call option gets more valuable, so the callable bond’s price falls (a putable bond’s price would rise, since the put adds value). The “tell” that an answer hinges on call risk is any mention of rising volatility or the call moving toward the money.

The trap is confusing call risk with convexity mechanics. Callable bonds show negative convexity only at low yields, where the call is near/in-the-money; at high yields the call is far out-of-the-money and they behave like straight bonds with normal positive convexity. Don’t equate “callable” with “putable” — the put protects the holder and adds value for them. Memory hook: whoever owns the option gains, so the issuer’s call is subtracted.