Question

The following European options are traded on the market Option Type Strike Put $40 Put $45 Put $50 Call $45 Call $50 Assume that all options are on one share of stock and all have three months left to expiration. The stock is currently traded at $44.50.

a. Investor A believes that in three months the stock price is going to decrease from the current level, but will not fall below $40. Suggest an option trading strategy that would be best suited to take advantage of this price movement. Explain how to set up this strategy using appropriate options from the table above. Clearly identify which option(s) should be bought and which one(s) should be sold.

b. Investor B has an opposite opinion and believes that in three months the stock price is going to increase but will not exceed $50. Suggest an option trading strategy that would be best suited to take advantage of this price movement. Explain how to set up this strategy using appropriate options from the table above. Clearly identify which option(s) should be bought and which one(s) should be sold.

c. Investor C disagrees with investors A and B and believes that in the next three months the stock price is going to stay around its current level. Suggest an option trading strategy that would be best suited to take advantage of this price movement. Explain how to set up this strategy using appropriate options from the table above. Clearly identify which option(s) should be bought and which one(s) should be sold.

d. Suppose that investors A, B, and C set up the trading strategies you constructed in parts a., b., and c., respectively. In three month, the price of stock ends up being $46. Calculate payoffs of each of the three strategies from parts a., b., and c.

Answer 1

Put $40 Put $45 Put $50 Call $45 Call $50

Current stock price $44.50

Investor A- Bear Spread Strategy. Buy Put $45 and Sell Put$40.

Investor B- Bull spread strategy. Buy call $45 and Sell Call$50

Investor C – Short Straddle Strategy. Sell Call$45 and Sell Put$45.

Stock price after 3 months - $46

Investor A’s Payoff: Both puts are out-of-money. None of them will be exercised. Payoff is $0.

Investor B’s Payoff: Call$45 is in-the-money and Call $50 ot-of-money. Only call$45 will be exercised.

Payoff from call$45 is (0, max($46-$45)) = $1.

Investor C’s Payoff: Payoff only on in-the- money Call$45. Payoff will be negative as the option was sold. Payoff is -$1. (same calculation in investor B payoff)

Note: Profit of each strategy is fully calculated after taking into account premiums also.