Callable bonds with no lockout period

Imagine a situation: a bond is being traded on market with no lockout period. It can be called at par (100) at any year.

We go from right to the left to calculate its price like in binominal trees. If its price is 100.19 at Year 2, for example, it turns into 100, because it would be called at 100. Then we get a price of 100.14 at Year 1 and it also turns to 100 for the same reason.

Next step is to discount to Year 0. We get bond price of 100.55. The question is why at Year 0 bond’s price is not 100, if it has no lockout period and can also be called at Year 0 at par.

If the price is above 100, then, using your phrase, it turns into 100. Easy peasy.