What are Call Options?
Option gives the holder (buyer/ one who is long call), the right to buy a specified quantity of the underlying asset at the strike price on the expiration date. The seller (one who is short call) however, has the obligation to sell the underlying asset if the buyer of the call option decides to exercise his option to buy.
Example: An investor buys One European call option on Stock "A" at the strike price of Rs. 3500 at a premium of Rs. 100. If the market price of Stock "A" on the day of expiry is more than Rs. 3500, the option will be exercised. The investor will earn profits once the share price crosses Rs. 3600 (Strike Price + Premium i.e. 3500+100). Suppose stock price is Rs. 3800, the option will be exercised and the investor will buy 1 share of Stock "A" from the seller of the option at Rs 3500 and sell it in the market at Rs 3800 making a profit of Rs. 200 {(Spot price - Strike price) - Premium}.
LONG CALL PAYOFF
Payoff is the cash flow that occurs at expiration. The long call can either exercise or not exercise.The long call's payoff will never be less than zero. Instead, the long call earns the larger of two possible payoffs, either ST — K or zero.
The payoff associated with a long call is, therefore, the following:
- If the long call exercises then the payoff is the difference between the price of the underlying asset that the long call receives and the strike price that it pays.
- If the long call does not exercise then the payoff is zero as no transaction takes place.
The difference between the underlying asset price and the strike price is the call option's “intrinsic value.” A call option only has intrinsic value when the underlying asset price is greater than the strike price. Otherwise, the intrinsic value of a call option is zero.
An equation that describes the payoff to the long call is:
Long call payoff = max(ST — K, O)
The output of the max( ) function is the larger of the two values on either side of the comma within the function.
Let's explore the equation for the payoff at expiration associated with a long call. Let's define the following notation:
T = Expiration date
ST = Underlying asset price at time T
K = Strike price
Consider the following example:
■ Strike price = $125
■ Underlying asset price at expiration = $135
The payoff is:
Long call payoff = max(ST − K, 0)
= max($135–$125, 0)
= $10
Consider another example:
■ Strike price = $823
■ Underlying asset price at expiration = $721
The payoff is:
Long call payoff = max(ST − K, 0)
= max($721–$823, 0)
= 0
The payoff of zero indicates that the long call will not exercise the option.
LONG CALL P&L
The long call's P&L and its relationship to the underlying asset price are detailed. The notation c0 is defined as follows:
Call premium paid by long call to the short call at initiation. The long call option's P&L at expiration can be expressed as:
Long call P&L
max(ST — K, 0) - c0
A positive value for the long call's P&L represents profit, and a negative value represents loss.
Consider the following example:
■ Strike price = $145
■ Underlying asset price at expiration = $154
■ Call premium paid at initiation = $8
The P&L is:
Long Call P&L = max(ST − K, 0) − c0
= max($154–$145, 0) − $8
= $1
Consider another example:
■ Strike price = $112.50
■ Underlying asset price = $113.00
■ Call premium paid at initiation = $7
The P&L is:
Long Call P&L = max(ST − K, 0) − c0
= max($113–$112.5, 0) − $7
= −$6.5
The long call’s breakeven point is where the price of the underlying asset that is received is equal to the combination of both the premium and strike price paid:
Long call breakeven∶ST = K + c0
For example,
consider the following scenario:
■ Initiation = June 1
■ Expiration = July 1
■ Strike price = $75
■ Call premium = $10
On June 1 we do not know what the underlying asset price will be on July 1. If the underlying asset price is less than $75 then the P&L will be −$10 representing a loss equal to the premium paid. The breakeven point occurs when the underlying asset price is $75 + $10 = $85.
SHORT CALL PAYOFF
A short call is obligated to sell the underlying asset to the long call should the long call exercise its right to purchase. The short call has no choice in the matter, because whether the transaction takes place or not completely depends on the long call's decision. The long call's choices at expiration, and their impact on the short call's payoff, are as follows:
M The long call exercises: The long call will exercise at expiration when the underlying asset price is greater than the strike price. In this see-nario the price of the underlying asset that the short call must deliver is greater than the strike price that the short call receives, and the short call's payoff is negative.
M The long call does not exercise: If the underlying asset price is less than
the strike price, the long call will not exercise, and the short call's payoff is zero.
The short call's payoff can be expressed as:
Short call payoff min(K — ST, 0)
The output of the min( ) function is the smaller of the two values on either side of the comma within the function.
Consider the following example:
■ Strike price = $125
■ Underlying asset price at expiration = $135
The payoff is:
Short call payoff = min(K − ST, 0)
= min($125 − $135, 0)
= −$10
Consider another example:
■ Strike price = $823
■ Underlying asset price at expiration = $721
The payoff is:
Short call payoff = min(K − ST, 0)
= min($823 − $721, 0)
= 0
SHORT CALL P&L
We've seen that the payoff associated with a short call is either zero or negative. If so, when does the short call profit? The answer is that the short call's P&L takes into account the premium that the short call receives at initiation.
The short call's P&L and its relationship to the long call's exercise decision are summarized. The short call's P&L at expiration can be expressed as:
Short call P&L min(K - ST, 0) + c0
A positive value for the short call's P&L represents profit while a negative value represents loss.
Consider the following example:
■ Strike price = $145
■ Underlying asset price = $154
■ Call premium paid at initiation = $8
The short call’s P&L is:
Short call P&L = min(K − ST, 0) + c0
= min($145 − $154, 0) + $8
= −$1
Consider another example:
■ Strike price = $112.50
■ Underlying asset price = $113.00
■ Call premium paid at initiation = $7
The short call’s P&L is:
Short call P&L = min(K − ST, 0) + c0
= min($112.5 − $113, 0) + $7
= $6.5
CALL OPTIONS ARE ZERO-SUM GAMES
Call options are zero-sum games. This means that any profit that one of the counterparties receives is exactly equal to the loss that the other counterparty suffers. This is true whether or not the long call exercises, as shown in.
For example,
consider the following scenario:
Call premium = $5
Strike price = $75
Underlying asset price at expiration = $85
The P&L is:
Long call P&L = max(ST - K, 0) - c0 = max($85 - $75, 0) - $5 = $5
Short call P&L min(K - ST, 0) + c0 = min($75 - $85, 0) + $5 = -$5
The net P&L across the long and short calls is: Net call P&L long call P&L + short call P&L
$5 - $5 = 0
CALL OPTION MONEYNESS
“Moneyness” is whether a long option position will earn a positive payoff if it exercises. The moneyness of an option is one of the following: M In-the-money (ITM) M Out-of-the-money (OTM) & At-the-money (ATM)
Let's explore each:
- ITM: An option is ITM when the long position will earn a positive pay- off if it exercises the option. A call option is ITM when the value of the underlying asset is greater than the strike price.
- OTM: An option is OTM when the long position will earn a negative payoff if it exercises the option. A call option is OTM when the value of the underlying asset is less than the strike price. A long call will not exercise an OTM option to avoid the negative payoff.
- ATM: An option is ATM if the long position will earn a payoff of zero if it exercises the option. A call option is ATM when the value of the asset is equal to the strike price. The long call is indifferent about choosing to exercise an ATM option since the long call earns a payoff of zero whether it exercises or not.
Reference
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