# Callable (Putable) Values as yields Increase (Decrease)

I know that “value of callable bond = value of option free - value of the call” I know that “When interest rates increase the value of a callable bond decreases less than an option free bond due to the value of the call option.” But just to put an example with it, is this example correct? non callable bond is trading at \$1000 and option value is \$50, so value of callable: 950 = 1000 - 50 So if rates increase and value of non callable is \$950, would the value of the call option move down, to say \$45, so the callable value would be: 905 = 950 - 45 so the non callable decreased \$50 while the callable only decreased \$45? Is that correct? For Putable bonds, my notes say “as yields fall, putable bond acts like option free.” Does this mean the prices between non-putable and putable will be exactly the same when rates decrease? If so, how come?

self-pity bump. I know there are similar discussions currently on page 1, and I’ve used the search function, but never see numbers or examples associated with these concepts.