Please answer the following using the case $-$ "Citic Tower II$".$ Assume no dividend payment. This is a group assignment for people who are in groups.

i$)$ What are the values of S$0,$ X $($strike$),$ t$,$ sigma, and the risk$-$free rate $($refer to the slides for the meanings of S$0,$ X$,$ t$,$ sigma as appropriate for a regular option$)$ for the option involved? Show calculations $($e$.$g$.,$ sigma$)$ for each variable, if required. Sigma should be annualized $($i$.$e$.,$ find the yearly sigma value$).(15$ points$)$

ii$)$ What kind of option $($call$/$put$,$ long$/$short$)$ is involved for the parties involved in the case? Briefly discuss how you decided on this $($i$.$e$.,$ compare the features of an option to the characteristics from the case$).$ The same option could mean different positions to the seller and the buyer. $(10$ points$)$

iii$)$ What is the price of the option? Use a $4-$step binomial tree to find the value of the option $($Assignment $8$ has a similar question to this$).$ Answer the following for this.

a$)$ Find u$,$ d$,$ and q$.(5$ points$)$

b$)$ Draw the stock tree, including the price at each node. $(5$ points$)$

c$)$ Find the terminal value of the option. $($there should be $5$ terminal values$)(5$ points$)$

d$)$ Find the value of the option at intermediate nodes. $($there should be $9$ intermediate nodes$)(18$ points$)$

e$)$ Find the value of the option at time $0.(2$ points$)$

iv$)$ Including the option, does the project look like a good investment $($need to find the expanded NPV for this$)?(5$ points$)$

v$)$ Should CPL accept the offer from the seller for the option? $($this requires a comparison of $5\%$ equity stake to the price of the option$)(5$ points$)$

vi$)$ What are the key lessons from this case? $(10$ points$)$