Call option and put option strategies

Let's first review the important notations:

c₀, c_T = price of call option at time 0 and time T

p₀, p_T = price of put option at time 0 and time T

X = exercise price

S₀, S_T = price of the underlying at time 0 and time T

V₀, V_T = value of the position at time 0 and time T

∏ = profit from the transactions

r = risk-free rate

Buying call option: The value of the call option at expiration will be equal to Max(0, S_T - X)

The value of the call option if the stock price is greater than the exercise price at expiration = S_T - X

The value of the call option if the stock price is lesser than or equal to the exercise price at expiration = 0

The profit from the long call strategy = Value at expiry - Premium paid for the call option = V_T - c₀ = c_T - c₀

The profit increases with the increase in the value of the underlying. So, the maximum profit is infinite.

The maximum loss for the long call position is when the option expires worthless, and the loss will be equal to the premium paid for the option.

The breakeven price will be the price where the trader will be able to recover the premium paid for the call option and that price will be equal to X + c₀.

Payoff graph:

Selling call option: The value and profit of the short call position will be exactly opposite to that of the long call position.

The maximum gain of the short call position will be equal to the maximum loss of the long call position and will be equal to the premium received by the option seller from the option buyer.

The maximum loss of the short call position will be equal to the maximum gain of the long call position and will be equal to the infinity.

The breakeven price for both the long call position and the short call position will be the same because both parties will have zero profit and zero loss at that price. And that price will be equal to X + c₀.

Payoff graph:

Buying put option: The value of the put option at expiration will be equal to the Max(0, X - S_T)

The value of the put option if the stock price is greater than or equal to the exercise price at expiration = 0

The value of the call option if the stock price is lesser the exercise price at expiration = X - S_T

The profit from the long put strategy = Value at expiry - Premium paid for the call option = V_T - p₀ = p_T - p₀

The profit increases with a decrease in the value of the underlying. The minimum value of the underlying is zero. So, the maximum profit of the put option equals X - S_T - p₀= X - 0 - p₀ = X - p₀.

The maximum loss for the long put position is when the option expires worthless and the loss will be equal to the premium paid for the option.

The breakeven price will be the price where the trader will be able to recover the premium paid for the put option and that price will be equal to X - p₀. Notice that the breakeven price is also equal to the maximum profit possible for the long put position because at this price, the profit is zero. And the stock's fall in price is limited by only this amount to give the maximum profit.

Payoff graph:

Selling put option: The value and profit of the short put position will be exactly opposite to that of the long put position.

The maximum gain of the short put position will be equal to the maximum loss of the long put position and will be equal to the premium received by the option seller from the option buyer.

The maximum loss of the short put position will be equal to the maximum gain of the long put position and will be equal to the exercise price X - p₀.

The breakeven price for both the long put position and the short put position will be the same because both parties will have zero profit and zero loss at that price. And that price will be equal to X - p₀.

Payoff graph:

Check your concepts:

(59.1) The breakeven price of a short put position is $45.00 for a stock. The premium received for the put position is $2.50. What will be the profit on the position at expiration if the stock ends at $46.50?

(a) -$1.00
(b) $1.50
(c) $2.50

(59.2) What will be the maximum profit for a long put position with $120 as the exercise price? The stock was trading at a price of $125 when the put option was bought. The premium paid for the put option was $3.

(a) $117
(b) $120
(c) $122

(59.3) Which of the following factors is least likely to impact the breakeven price of a call option?

(a) Call premium
(b) Exercise price of the call option
(c) Spot price at expiration

(59.4) Which of the following call options is most likely to have the higher maximum profit for the short position if the positions are initiated at the same time?

(a) Exercise price of $30
(b) Exercise price of $32
(c) Exercise price of $34

Solutions:

(59.1) Correct Answer is B: The breakeven price for a short put position is equal to the exercise price minus the premium paid for the put option. Therefore, X - 2.5 = 45 =>X = $47.50. Value of put option at expiration = Max(0, X-ST) = 47.50 - 46.50 = $1.00. Profit for the short position = Put premium - Value of put option = 2.50 - 1.00 = $1.50. Or the profit of a short put option equals spot price at expiration minus breakeven price.

(59.2) Correct Answer is A: The maximum profit for a long put option is equal to the exercise price minus the premium paid for the put option. Therefore, the maximum profit for the long put position = 120 - 3 = $117.

(59.3) Correct Answer is C: The breakeven price of a call option is equal to the exercise price plus the call premium. The spot price at the expiration does not impact the breakeven price calculation.

(59.4) Correct Answer is A: The maximum profit for a short call position is the premium received for the call option. The premium of the call option with the lowest exercise price will be maximum.

Next LOS: Covered call and protective put strategies