We calibrate binomial tree, because in the exercise tasks (or in the market data) we have just spot rates and we need forward rates. Those spot rates are the spot rates from now until a particular maturity. We need forward rates, because current forward rates are the best estimator for the future one-year spot rates. True?
What I don’t understand is that the values of the bonds in the binomial tree seem to be discounted by a “too early forward rate”. Anyone knows the reason why we assign the discount rates “too early”?
Deriving forward rates from spot rates and calibrating a binomial tree are two very different things.
Yes.
According to one yield curve theory (pure expectations), today’s forward rates are estimates of future spot rates. As far as I know, they are not necessarily considered to be the best estimators of future spot rates. So that’s not true.
Furthermore, that’s not the reason we need forward rates. We need forward rates for the binomial tree so that we can discount one period at a time, which allows us to adjust the cash flows each period based on our estimate of whether or not they will change (because, for example, an option will be exercised).
I don’t know what you mean by “too early”. The forward rate at a node is the rate calculated to discount a payment from one period in the future back to the time at that node. It isn’t too early.