Use this information for problems through $24.$ The stock was priced at $165\mathrm{.}13.$ The expirations are July $17,$ August $21,$ and October $16.$ The continuously compounded risk$-$free rates associated with the three expirations are $0\mathrm{.}0503,0\mathrm{.}0535,$ and $0\mathrm{.}0571,$ respectively. The standard deviation is $0\mathrm{.}21.$

a$.$ Construct a bear money spread using the Octo$-$

ber $165$ and $170$ calls. Hold the position until the

options expire. Determine the profits and graph

the results. Identify the breakeven stock price at

expiration and the maximum and minimum

profits. Discuss any special considerations asso$-$

ciated with this strategy.

b$.$ Repeat problem $"$a$.",$ but close the position on

September $20.$ Use the spreadsheet to find the

profits for the possible stock prices on September

Generate a graph and use it to identify the

approximate breakeven stock price.