The value of a callable bond is the value of the bond minus the value of the call option. I’m just finishing up derivatives right now so i can’t immediately recall all the details of the fixed income but as I recall;

You set up the bond valuation using the binomial process i.e. up and down movements. Except at each node the value may change depending on where interests have moved; it can be advantageous for the company to call the bond when interest rates have dropped below the current coupon. When this happens you set the value of the node equal to what the bond should be called for. With callable bonds, the valuation will be sensitive to what the prepayment assumptions are.

Using the traditional backwardation method, you then value the bond discounting each node until you reach t0.

Thats the best explanation i can give,

I hope it helps

Thanks for your help, Harry!