Jane Joseph, a manager at Computer Science, Inc. $($CSI$),$ received $1,000$ shares of com$-$pany stock as part of her compensation package. The stock currently sells at $$40$ a share. Joseph would like to defer selling the stock until the next tax year. In January, however, she will need to sell all her holdings to provide for a down payment on a new house. Joseph is worried about the price risk involved in holding on to the shares. At current prices, she would receive $$40,000$ for the stock. If the value of her stock holdings falls below $$35,000,$ her ability to come up with the necessary down payment would be jeopardized. On the other hand, if the stock value rises to $$45,000,$ she would be able to maintain a small cash reserve even after making the down payment. Joseph considers three investment strategies:

a$)$ S trategy A is to write January call options on the CSI shares with strike price $$45.$ These calls are currently selling for $$3$ each.

b$)$ S trategy B is to buy January put options on CSI with strike price $$35.$ These options also sell for $$3$ each.

c$)$ S trategy C is to establish a zero$-$cost collar by writing the January calls and buying the January puts.