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 $$25.$ If six months later, the stock price per share is $$25$ or more, the option has no value. If in six months the stock price is lower than $$25$ per share, then you can purchase the stock and immediately sell it at the higher exercise price of $$25.$ If the price per share in six months is $$22\mathrm{.}50,$ you can purchase a share of the stock for $$22\mathrm{.}50$ and then use the put option to immediately sell the share for $$25.$ Your profit would be the difference,

$$25$ $$22\mathrm{.}50=$ $$2\mathrm{.}50$

per share, less the cost of the option. If you paid $$1\mathrm{.}00$ per put option, then your profit would be

$$2\mathrm{.}50$ $$1\mathrm{.}00=$ $$1\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 $210$ shares of the stock at $$27$ per share and $70$ six$-$month European put options with an exercise price of $$25.$ 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.$

A B C D

$1$ European Put Option

$2$ Share Price Value with Options Value without Options

$3$ $$15\mathrm{.}00$ $

$10\mathrm{.}00$

Changed: Your submitted answer was incorrect. Your current answer has not been submitted.

$

$4$ $$16\mathrm{.}00$ $

Incorrect: Your answer is incorrect.

$

$5$ $$17\mathrm{.}00$ $

$

$6$ $$18\mathrm{.}00$ $

$

$7$ $$19\mathrm{.}00$ $

$

$8$ $$20\mathrm{.}00$ $

$

$9$ $$21\mathrm{.}00$ $

$

$10$ $$22\mathrm{.}00$ $

$

$11$ $$23\mathrm{.}00$ $

$

$12$ $$24\mathrm{.}00$ $

$

$13$ $$25\mathrm{.}00$ $

$

$14$ $$26\mathrm{.}00$ $

$

$15$ $$27\mathrm{.}00$ $

$

$16$ $$28\mathrm{.}00$ $

$

$17$ $$29\mathrm{.}00$ $

$

$18$ $$30\mathrm{.}00$ $

$

$19$ $$31\mathrm{.}00$ $

$

$20$ $$32\mathrm{.}00$ $

$

$21$ $$33\mathrm{.}00$ $

$

$22$ $$34\mathrm{.}00$ $

$

$23$ $$35\mathrm{.}00$ $

$

$24$

$25$

$($b$)$

Discuss the value of the portfolio with and without the European put options.

The lower the stock price, the

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beneficial the put options. The options are worth nothing at a stock price of $

or

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$.$ There is a benefit from the put options to the value of the portfolio for stock prices $

or

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$.$