Given a variability of \(\sigma=\sqrt{h V_{e}^{A}}=0.10\) and current one- and two-period spot rates of \(S^{m}{ }_{1}=0.07\) and \(S^{m}{ }_{2}=0.0804\) :

a. Generate a one-period binomial interest rate tree using the calibration model. (Hint: Try \(S_{d}=0.08148\).)

b. Using the calibrated tree, determine the equilibrium price of a two-period, option-free, \(10.5 \%\) coupon bond \((F=100)\).

c. Does the binomial tree price the \(10.5 \%\) option-free bond equal to the bond's equilibrium price? Comment on this feature of the calibration model.