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 $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $25. Your profit would be the difference, $25 $22.50 $2.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $2.50 - $1.00 = $1.50 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 290 shares of the stock at $29 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 $1.00. (a) Using data tables, construct a model that shows the value of the portfolio with options and with increments of $1.00. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 18 19 20 Share Price $15.00 $16.00 $17.00 $18.00 $19.00 $20.00 $21.00 $22.00 $23.00 $24.00 $25.00 $26.00 $27.00 $28.00 $29.00 $30.00 $31.00 $32.00 $ $ $16 $ $ $ $ $ $ $ $ $ S S S S S S B European Put Option Value with Options $ $ $ $ $ S $ 13 Value without Options $ 15 X $ $ $ $ $ $ $ C 12 13 14 15 16 17 18 19 20 21 22 23 24 25 $24.00 $25.00 $26.00 $27.00 $28.00 $29.00 $30.00 $31.00 $32.00 $33.00 $34.00 $35.00 $ $ LA $ LA $ 69 69 $ $ LA $ LA 69 $ 69 $ 69 6.9 $ $ 69 69 $ $ $ (b) Discuss the value of the portfolio with and without the European put options. The lower the stock price, the more beneficial the put options. The options are worth nothing at a stock price of $ benefit from the put options to the value of the portfolio for stock prices $ or lower > 2 or higher There is a