Use this information for problems $6$ 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 $0\mathrm{.}21.$

$\backslash$table$[[,$Calls,,Puts$],[$Strike$,$Jul,Aug,Oct,,Jul,Aug,Oct,$],[160,6\mathrm{.}00,8\mathrm{.}10,11\mathrm{.}10,,0\mathrm{.}75,2\mathrm{.}75,4\mathrm{.}50,],[165,2\mathrm{.}70,5\mathrm{.}25,8\mathrm{.}10,2\mathrm{.}40,4\mathrm{.}75,6\mathrm{.}75,,],[170,0\mathrm{.}80,3\mathrm{.}25,6\mathrm{.}00,5\mathrm{.}75,7\mathrm{.}50,9\mathrm{.}00,,]]$

Construct a bear money spread using the October $165$ 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 associated with this strategy.

Problem $(7)$ darr

Repeat problem $6,$ but close the position on September $20.$ Use the spreadsheet to find the profits for the possible stock prices on September $20.$ Generate a graph and use it to identify the approximate breakeven stock price.

dedermine the prefits for the prices of $150,155,...180$