Question
In: Finance
Call options on a stock are available with strike prices of $15, $17.5, and $20 and...
Call options on a stock are available with strike prices of $15, $17.5, and $20 and expiration dates in 3-months. Their prices are $4, $2, and $0.5, respectively. An investor creates a portfolio by buying call options with strike prices of $15 and $20 and selling 2 call options with strike prices of $17.5.
a. Construct a table showing how profit varies with the stock price for this portfolio.
b. Plot the payoff diagram?
Solutions
Expert Solution
a)
Profit from Long Call option with Strike of $15 = max(Stock Price - Stirk Price, 0) - Call premium
Profit from Long Call option with Strike of $15 = max($13 - $15, 0) - $4
Profit from Long Call option with Strike of $15 = -$4
Profit from Long Call option with Strike of $20 = max(Stock Price - Stirk Price, 0) - Call premium
Profit from Long Call option with Strike of $20 = max($13 - $20, 0) - $0.5
Profit from Long Call option with Strike of $20 = -$0.5
Profit from 2 Short Call option with Strike of $17.5 = 2 * (- max(Stock Price - Stirk Price, 0) + Call premium)
Profit from 2 Short Call option with Strike of $17.5 = 2 * ( - max($13 - $17.5, 0) + $2)
Profit from 2 Short Call option with Strike of $17.5 = $4
| Stock Price | Profit from Long Call option with Strike = $15 | Profit from Long Call option with Strike = $20 | Profit from 2 Short Call option with Strike = $17.5 | Total Profit |
| $13.00 | -$4.00 | -$0.50 | $4.00 | -$0.50 |
| $13.50 | -$4.00 | -$0.50 | $4.00 | -$0.50 |
| $14.00 | -$4.00 | -$0.50 | $4.00 | -$0.50 |
| $14.50 | -$4.00 | -$0.50 | $4.00 | -$0.50 |
| $15.00 | -$4.00 | -$0.50 | $4.00 | -$0.50 |
| $15.50 | -$3.50 | -$0.50 | $4.00 | $0.00 |
| $16.00 | -$3.00 | -$0.50 | $4.00 | $0.50 |
| $16.50 | -$2.50 | -$0.50 | $4.00 | $1.00 |
| $17.00 | -$2.00 | -$0.50 | $4.00 | $1.50 |
| $17.50 | -$1.50 | -$0.50 | $4.00 | $2.00 |
| $18.00 | -$1.00 | -$0.50 | $3.00 | $1.50 |
| $18.50 | -$0.50 | -$0.50 | $2.00 | $1.00 |
| $19.00 | $0.00 | -$0.50 | $1.00 | $0.50 |
| $19.50 | $0.50 | -$0.50 | $0.00 | $0.00 |
| $20.00 | $1.00 | -$0.50 | -$1.00 | -$0.50 |
| $20.50 | $1.50 | $0.00 | -$2.00 | -$0.50 |
| $21.00 | $2.00 | $0.50 | -$3.00 | -$0.50 |
| $21.50 | $2.50 | $1.00 | -$4.00 | -$0.50 |
| $22.00 | $3.00 | $1.50 | -$5.00 | -$0.50 |
b)
| Stock Price | Payoff from Long Call option with Strike = $15 | Payoff from Long Call option with Strike = $20 | Payoff from 2 Short Call option with Strike = $17.5 | Total Payoff |
| $13.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| $13.50 | $0.00 | $0.00 | $0.00 | $0.00 |
| $14.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| $14.50 | $0.00 | $0.00 | $0.00 | $0.00 |
| $15.00 | $0.00 | $0.00 | $0.00 | $0.00 |
| $15.50 | $0.50 | $0.00 | $0.00 | $0.50 |
| $16.00 | $1.00 | $0.00 | $0.00 | $1.00 |
| $16.50 | $1.50 | $0.00 | $0.00 | $1.50 |
| $17.00 | $2.00 | $0.00 | $0.00 | $2.00 |
| $17.50 | $2.50 | $0.00 | $0.00 | $2.50 |
| $18.00 | $3.00 | $0.00 | -$1.00 | $2.00 |
| $18.50 | $3.50 | $0.00 | -$2.00 | $1.50 |
| $19.00 | $4.00 | $0.00 | -$3.00 | $1.00 |
| $19.50 | $4.50 | $0.00 | -$4.00 | $0.50 |
| $20.00 | $5.00 | $0.00 | -$5.00 | $0.00 |
| $20.50 | $5.50 | $0.50 | -$6.00 | $0.00 |
| $21.00 | $6.00 | $1.00 | -$7.00 | $0.00 |
| $21.50 | $6.50 | $1.50 | -$8.00 | $0.00 |
| $22.00 | $7.00 | $2.00 | -$9.00 | $0.00 |
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