callable bond option

It is said in the text when interest rate rises, callable bond option(embeded) decreases but as normal call option, when interest rate rises, call option rises, why interest rate option is different?

This is on a BOND. When Interest rate rises - Bond Price reduces… doesn’t that make any difference at all?

oh,no no, as interest rate rises, price decrease, but (1+r)^T also rises, so why option decreases? option=S-X/(1+r)^t

Spot price reduced. S reduced… so overall your call option price reduced…

Simply put: The “call” portion of a “callable” bond is actually owned by the issuer. The question you’re asking refers to the value of the bond to the investor. Thus, as interest rate volatility rises, the value of that call does become more valuable - to the issuer. Since there are no free lunches, that value comes from somewhere - that somewhere being out of the pockets of the investor. Put another way: The investor is actually short a call on the bond.

The way I look at it is, if interest rates drop, if I’m the borrower, I’m more likely to call the bond so I can reissue debt at a lower interest rate. This makes the call option more valuable to me but in the marketplace, it would cause the price to drop because to people looking to buy the bond, they know it could be called. Conversely, if rates rise, i’m less likely to call the bond as I’m paying a lower coupon now than I would if I called it. Hence, the call option value goes down, but in the marketplace, that bond is worth a little more now because the likelihood of calling the bond is lessened. This is why you subtract the price of a call option from the price of a bond and add a put option price to the price of the bond. You should be able to analyze the value of a put option from the same perspective and understand why it’s more/less valuable with increase/decrease in interest rates.