$1.$ Suppose CM Capital is negotiating a financing deal with a hot startup firm. If the negotiation is successful, which will be known in three months, the venture capitalist is going to commit CNY$10,000,000$ as the first installment. To hedge the contingent exposure, the venture capitalist plans to buy options on Chinese yuan.

a$.$ What type of option should CM Capital buy, Call or Put? Why?

b$.$ Suppose the strike price of the option is $6\mathrm{.}90/$$; the call option premium is $$0\mathrm{.}007$ per yuan; the put option premium is $0\mathrm{.}009$ per yuan. What will CM Capital do in the following four scenarios and what$$s the payoff$/$payment in dollars in each scenario?

$(1)$ Negotiation is successful and spot rate is $6\mathrm{.}80/$$$.$

$(2)$ Negotiation is successful and spot rate is $7\mathrm{.}00/$$$.$

$(3)$ Negotiation fails and spot rate is $6\mathrm{.}80/$$$.$

$(4)$ Negotiation fails and spot rate is $7\mathrm{.}00/$$$.$