Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S9 / 3 / 4

At each time-2 node, replicate one positive put payoff using $\Delta$ shares and a current cash deposit $b$. Its two terminal values must satisfy $\Delta S_u+Rb=P_u$ and $\Delta S_d+Rb=P_d$, with $R=1.04$. ThusFor the three nodes the hedge isAt $S_2=121$, both child puts expire worthless. At $99$, the child payoffs are $0$ and $18.9$; at $81$, they are $18.9$ and $35.1$. Substituting the hedge holdings into both child states verifies those payoffs exactly.

The writer is short the option and therefore holds this positive replicating portfolio to offset the liability. At the lower nodes that means shorting shares and depositing the proceeds together with the option value, rather than buying positive-delta stock. Rebalancing the replicating holdings along the tree is self-financing in the ideal model; the combined short option plus hedge has zero terminal liability in either child state.