question regarding call option pricing

hey guys

i have a question regarding the pricing for callable bonds and i having some problems with it. usually wht they said is when the interst rate decreases the price of callable bond will increase and putable bond will decrease but my argument is tht the price of calllable bond cannot increase because as int rate will go down the issuer will redeem his bonds @ indenture call price and this will decrease the value of it so the other invester will not pay more than the stated call price or in other words it will have negative convexity… m i correct

thanks in advance

There are a few effects here and one is lots stronger than the others. When interest rates go down, the overwhelming effect on a bond is for the bond to increase in price. This is because the discount rates on the cash flows goes down. The presence of embedded options in the bonds muddies that a little but not that much. Callable bonds - Decreasing interest rates cause the price of the bond to go up at an ever slower rate. In general, the price of the bond will not rise above the call price if the bond is currently callable and will not rise much above the call price if it’s callable in the future. The rising at an ever slower rate is what’s meant by negative convexity. Puttable bonds - Here the owner of the bond has a put option. As interest rates deecrease the bond becomes more valuable because the discount rates on the cash flows goes down. This is the overwhelming big effect. If you own a puttable bond, you want interest rates to go down. However, your put option is also losing value as interest rates decrease because it is getting farther out of the money (also losing a little on rho). That means your puttable bond is not gaining as fast as it would if you didn’t have the put option.

@joey- i agree with u with call option explanation but u wrote the if u own puttable bond u want to int rate to go down shouldn’t it be the other way around. if the int rate decreases then the bond holder will not exercise the option in tht case it will become worthless…

No - if you own a puttable bond you want to make money owning the bond by having interest rates decrease. Think of the put option like an air bag in your car. You paid good money for that air bag and you will use it if you have to, but most people would be just fine going through life never seeing the air bag. The embedded put is like that. You will use it if interest rates go up, you would just like that not to happen.

i m srry joey i m getting ur concept i checked in the book and they haven’t mentioned tht point anywhere… maybe i m too tensed up for this kind of thing and belive me at this moment i cant learn any new concepts… but thanks for helping i really appreciated…