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@SeesFA,
I agree that the interest rate rise will affect both bonds.
But in terms of the call option, thinking of it as a stand alone option. Should not the rise in the rates cause the value of the call option to fall, since at each node the bond will be worth less, and thus less value for the call at each node…
and thus, if what i am saying about the price of call being affected by interest rates moving up, the effect on the callable bond becomes uncertain…
on the one hand the non-callable portion of it is going down..
but the call is also going down, which would make the callable worth more….

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