Consider a spot rate curve: 1% 1Yr, 2% 2Yr, 3% 3Yr. Suppose today issue a 3 year zero coupon bond, the price shall be 100 / (1+ 3%) ^3. My first question is, suppose the spot rate curve keeps the same going forward, after one year, what is the price of this zero coupon bond, will it be 100/(1+2%)^2?
If the answer to my first question is yes, then the return rate of the zero coupon bond for the first year is just the forward rate (1+3%)^3 / (1+2%)^2. Consider the short rate from Vasicek model, as the spot rate curve is upward sloping all the time, short rate r(t) should be decreasing towards the maturity of bond even the spot rate curve keeps the same. So I claim the movement of short rate in my example is the movement of rate along the forward rate curve, from year T=3 to T=0. Is my claim correct?
If the answer to the above is correct, as I see people calibrating the one factor Vasicek model by using a particular rate, ex. 3-mon Libor, isn't this incorrect?