Next, calculate the respective values $($again$,$ displayed to four decimal places$)$ for the components of the duplicating portfolio $($the "delta" and the amount of lending$)$ at the start of each period, for $t=0,1,2,3$ :

${}_t=\frac{P_{u,t+1}-P_{d,t+1}}{S_t(u-d)}$

$B_t=\frac{d{P}_{u,t+1}-u{P}_{d,t+1}}{(hat(r))(u-d)}$

Show that the value of the portfolio at each node $(V_t)$ matches the option value that you calculated, for the ten nodes corresponding to $t=0,1,2,3$ :

$V_t={}_t{S}_t-B_t$