Integrated cases: an underpriced put and a tree with a negative rate

In short

• Read the panel in order: the two end prices, the option's payoff in each state, the rate for the period (not the annual rate), then the quoted price.
• Get h* from the payoffs alone. For a put it is negative, so the put and the shares are bought (or sold) together.
• Value with $\pi = (1+r-R^d)/(R^u-R^d)$ and discount at $1+r$; cross-check by replication or put-call parity.
• An underpriced option is bought with its hedge. The hedge's riskless return is end value ÷ total outlay − 1, and it is compared with r, not with zero.
• A negative rate does not change a formula: $1+r$ is simply below 1, so π is lower and discounting adds value.