Options Strategies
Options, Futures and Derivative Securities
Spring 2025
What Is an Option Strategy?
- An option strategy involves combining an option with other assets, such as stocks and bonds, and/or other options together.
- The analysis that follows applies to European type options written on non-dividend paying stocks.
- Even though all strategies could be implemented using American type options, the payoff diagrams we present below might be affected by early exercise.
Covered Call
- A covered call consists in a long position in the stock and a short position in a European call option with strike K and maturity T.
Example 1: Covered Call
- A non-dividend paying stock currently trades at $50.
- A call option with strike $60 and maturity 3 months sells for $3.45.
- The cost of the covered call is 50 - 3.45 = $46.55.
- The payoff and profit for different stock prices at maturity is:
| Long Stock |
40 |
60 |
80 |
| Short Call |
0 |
0 |
-20 |
| Payoff |
40 |
60 |
60 |
| Profit |
-6.55 |
13.45 |
13.45 |
Covered Call
- The payoff of a covered call on a non-dividend paying stock can then be described as follows:
| Long Stock |
S |
S |
| Short Call |
0 |
-(S - K) |
| Covered Call |
S |
K |
- Therefore, the covered call pays like the stock if S \leq K and caps the payoff at K otherwise.
- This might be an interesting strategy if you think that the stock should go up in the near future but not that much.
Protective Put
- A protective put consists in a long position in the stock and a long position in a European put option with strike K and maturity T.
Example 2: Protective Put
- A non-dividend paying stock currently trades at $50.
- A put option with strike $40 and maturity 3 months sells for $1.28.
- The cost of the protective put is 50 + 1.28 = $51.28.
- The payoff and profit for different stock prices at maturity is:
| Long Stock |
30 |
50 |
70 |
| Long Put |
10 |
0 |
0 |
| Payoff |
40 |
50 |
70 |
| Profit |
-11.28 |
-1.28 |
18.72 |
Protective Put
- The payoff of a protective put on a non-dividend paying stock can then be described as follows:
| Long Stock |
S |
S |
| Long Put |
K - S |
0 |
| Protective Put |
K |
S |
- Therefore, the protective put pays like the stock if S > K and caps the payoff at K otherwise.
- This might be an interesting strategy if you want to hedge your portfolio from potential losses, although the hedge comes at a cost.
Straddle
- A straddle is a two-leg option strategy that consists in buying a call and a put with the same strike K.
Example 3: Straddle
- A non-dividend paying stock currently trades at $50.
- A put and a call with strike K = \$50 cost $4.68 and $7.12, respectively.
- The cost of the straddle is 4.68 + 7.12 = $11.80.
- The payoff and profit for different stock prices at maturity is:
| Long Put |
20 |
0 |
0 |
| Long Call |
0 |
0 |
20 |
| Payoff |
20 |
0 |
20 |
| Profit |
8.20 |
-11.80 |
8.20 |
Straddle
- The payoff of a straddle can then be described as follows:
| Long Put |
K - S |
0 |
| Long Call |
0 |
S - K |
| Straddle |
K - S |
S - K |
- The straddle pays off when the stock price moves significantly from the middle strike.
Strangle
- A strangle is a two-leg option strategy that consists in a long call with strike K_{2} and a long put with strike K_{1} where K_{1} < K_{2}.
Example 4: Strangle
- A non-dividend paying stock currently trades at $50.
- A put with strike K_{1} = \$45 trades for $2.65 whereas a call with strike K_{2} = \$55 costs $5.01.
- The cost of the strangle is 2.65 + 5.01 = $7.66.
- The payoff and profit for different stock prices at maturity is:
| Long Put |
15 |
0 |
0 |
| Long Call |
0 |
0 |
15 |
| Payoff |
15 |
0 |
15 |
| Profit |
7.34 |
-7.66 |
7.34 |
Strangle
- The payoff of a strangle can then be described as follows:
| Long Put |
K_{1} - S |
0 |
0 |
| Long Call |
0 |
0 |
S - K_{2} |
| Strangle |
K_{1} - S |
0 |
S - K_{2} |
- Compared to the straddle, the strangle requires the stock price to move even more in order to make a profit.
