A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you

to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase

a six$-$month European put option for a share of stock with an exercise price of $$27.$ If six months later, the stock price per share is $$27$ or more, the option has no

value. If in six months the stock price is lower than $$27$ per share, then you can purchase the stock and immediately sell it

the price per share in six months is $$23\mathrm{.}50,$ you can purchase a share of the stock for $$23\mathrm{.}50$ and then use the put option to immediately sell the share for $$27.$

Your profit would be the difference, $$27-$$$23\mathrm{.}50=$$$3\mathrm{.}50$ per share, less the cost of the option. If you paid $$1\mathrm{.}00$ per put option, then your profit would be

$$3\mathrm{.}50-$$$1\mathrm{.}00=$$$2\mathrm{.}50$ per share.

The point of purchasing a European option is to limit the risk of a decrease in the per$-$share price of the stock. Suppose you purchased $360$ shares of the stock at

$$31$ per share and $130$ six$-$month European put options with an exercise price of $$27.$ Each put option costs $$1.$

$($a$)$ Using data tables, construct a model that shows the value of the portfolio with options and without options for a share price in six months between $$15$ and

$$35$ per share in increments of $$1\mathrm{.}00.$

$($b$)$ Discuss the value of the portfolio with and without the European put options.

$($a$)$ Using data tables, construct a model that shows the value of the portfolio with options and without options for a share price in six months between $$15$

and $$35$ per share in increments of $$1\mathrm{.}00.$

Constructing data tables using Excel is a quick way to calculate expressions by substituting different values for one of the terms within a formula. Before using the

data table option, a spreadsheet of values and formulas must be constructed.

Open an Excel spreadsheet and format it as below. First place the known values in the spreadsheet. The exercise price is given to be $$27.$ At the end of $6$ months,

the price per share is $$23\mathrm{.}50.$ A total of $360$ shares were purchased at $$31$ per share. In addition, $130$ six$-$month European put options were purchased for $$1$

each. Place these values in the spreadsheet below.