I always get this confused and I always have such confidence that I can reason my way through this, but apparently I can’t… If rates decrease = price increase = value of a callable bond increases? Why? If the price increases wouldn’t the callable bond just be called away (say at par?) And if it’s called away wouldn’t this suck for the bondholder and thus the value of a callable bond decrease? Is my logic wrong somewhere? Can someone help me remember this correctly? 
hope I remeber this correctly callable bonds present negative convexity meaning that as rates decrease bond prices increases. as bond price approaches call price the bond price increases less and less in theory not going above the call price
Bonds will always increase in price as rates decrease, and just like florinpop said, callable bonds will approach the call price without going above it. So even for callable bonds for example, say its callable at 100, currently trading at 80, if rates fall, the price will rise, although the closer it gets to 100 the less it will increase price, hence the negative convexity.
Am i just burnt out or did you explain it …but not really explain it? haha…sorry… Right so the callable bond price increases less and less. Thus, there is essentially a cap on how much price appreciation there is …YOUR CAPPED…you can’t make any more moolah…so why is the callable bond actually more valuable when this happens? i don’t get it. Depressing, i thought I had this too. I’m losing it.
Its not more valuable if the price is at the call price. You are right about the cap, it won’t trade any higher than the call price in theory.
it becomes more valuable as interest go down and price goes up until the call price at call price if interest rates go down even more the value remains the same (value=price)
This is how i work it out: V(call option) = V(non callable) - V(callable). Options move in whatever direction interest rates go. Hence, when rates decrease, the call option decreases. V(call option) decreases as rates decrease. assume V(non callable) does not change, then, the only thing to satisfy the equation is V(callable) increases. Hence, when rates decrease, the value of the callable bond increases. also, V(put option) = V(putable) - V(non putable) as rates go up, the value of the put option goes up. Therefore, the only way to satisfy the equation (assuming V(non putable)) is constant is if V(putable) goes up.
> V(call option) decreases as rates decrease. assume > V(non callable) does not change I am not sure thats a good assumption to make. If the rates go down value of call option increases as the option here is on a bond. But with rates decrease value of non-callable also goes up. So both the components on RHS increase. Here is what I think happens when rates go down (can be wrong): As the rates go lower and lower the call option delta increases and moves closer to 1. So a $5 increase in bond price due to decrease in interest rate will lead to almost but not equal to $5 increase in call option value. This might explain a small change in the value of callable bond.
