Callable bonds vs option free bonds

In a callable bond, when yield curve shifts upwards;
Embedded short call option will decrease in value and this will partially offset losses on underlying bond.

Can someone explain this point? I understand that callable behaves like a option free bond when yields rise, so how is the loss offset?


Price callable = price of option free - value of call
Value of option free falss
value of call also decreases

Price callable still drops but by not by as much (in % terms)

Here still we are subtracting the options value regardless the decrease in options value right? So how does the fall in price is less compared to an option free bond when you’re subtracting the options value?

The option valuue will have decreased as yields increase so y0u are subtracting a lower number.

It is not going to make the oind go up in price just down less than if it had been an option free bond.

Option free
Before Priice = 99
After Prrce = 97
Change 2
Chnage% = 2/98 = 2.04%

Callable bond
Before = 99 - 1 = 98
After = 97 - 0.5 - 96.5
Change = 1.5
Chnage^ = 1.5/97 = 1.54%

Look at the diagram.

Thank you, I think I get it now. Can you please tell me if the below statements are true?

• When rates rise, putable bonds price falls the least, & callable bonds fall less in value than option free bonds.
• When rates fall, callable bonds price rises the least, & the rise in putable bonds price is less than rise in option free bonds.