Interest rate volatility

How is the value of a straight bond unaffected by interest rate volatility?? I suppose binomial model is used to represent the interest rate volatility, calibrate the interest rates, and calculate the bond value. So, using the spot rates 3, 4, 5, on a 2-year 6% bond, we get the value, which should be different if the spot rates are 3,3,3 (which I suppose is the flat yield curve because the spot rates are same)…

So, because the spot rates change, ie, the yield curve is upward sloping, are not the interest rates volatile? And due to this volatility, the bond price is changing?

Even if I use the binomial model forward rates, the volatility will be used to calculate the adjacent forward rates, which decide the value. If the volitality changes, the value of the bond would too.

Can anyone explain how the value is unaffected?

Someone clear the doubt please!

When you increase the interest rate volatility in a binomial interest rate tree you recalibrate it so that it prices par bonds (at all maturities) correctly. This ensures that the effective average spot rate at each maturity is equal to the rate on the (zero-volatility) spot curve at that maturity.