ABC Brokers has today written a new European option on stock issued by Dannevirke & Eketahuna Finance $($DEF$).$ The option expires in one year's time. A price for the option has been determined via the calculation shown in the following diagram. Each time step in the diagram represents $3$ months. The assumed risk$-$free interest rate is $6\%$ per annum, continuously compounded.

$($a$)$ What type of option is this? What is its strike price?

$($b$)$ Fill in the missing value denoted $H$ in the diagram.

$($c$)$ Fill in the missing value denoted $P$ in the diagram.

$($d$)$ The risk$-$neutral probability used in this calculation is the same at every point in the diagram. What is the value of this probability?

$($e$)$ Suppose ABC Brokers wishes to hedge the risk associated with writing this option. Should it initially buy DEF stock, or sell it short? How many shares should be bought or sold short?