Consider a 3-year putable bond with 7% coupon rate which becomes putable at $101 in one year and stays putable at $101 in the following years. As in the following exhibit the prices for an option-free bond in the second year are calculated as $99.115, $100.295, and $101.282 in upper, middle and lower nodes. Assume P_H=P_L=0.50. Here is the binomial tree and valuation for this bond

What is the modified price at Price at N_HL when we consider that this bond is putable?

What is the modified price at Price at N_LL when we consider that this bond is putable?

\begin{tabular}{|c|c|c|c|} \hline t=0 & t=1 & t=2 & t=3 \\ \hline & & & \\ \hline & & & \\ \hline & & & V=$100 \\ \hline & & & C=$7 \\ \hline & & & \\ \hline & & V=$99.115 & \\ \hline & & C=$7 & \\ \hline & & r2,t+1=7.955% & \\ \hline & V= & & V=$100 \\ \hline & C=$7 & & C=$7 \\ \hline & r1,H=7.2% & & \\ \hlineV= & & V=$100.295 & \\ \hlineC=0 & & C=$7 & \\ \hline \multirow[t]{9}{*}{r0=4.45%} & & r2,H=6.685% & \\ \hline & V= & & V=$100 \\ \hline & C=$7 & & C=$7 \\ \hline & r1,L=5.395% & & \\ \hline & & V=$101.282 & \\ \hline & & C=$7 & \\ \hline & & r1,u=5.646% & \\ \hline & & & V=$100 \\ \hline & & & C=$7 \\ \hline \end{tabular}