Options Strategies

Options and Futures

Lorenzo Naranjo

Spring 2024

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:

Stock Price	40	60	80
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:

	\(S \leq K\)	\(S > K\)
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:

Stock Price	30	50	70
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:

	\(S \leq K\)	\(S > K\)
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:

Stock price	30	50	70
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:

	\(S \leq K\)	\(K < S\)
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:

Stock Price	30	50	70
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:

	\(S \leq K_{1}\)	\(K_{1} < S \leq K_{2}\)	\(K_{2} < S\)
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.