Options Payoffs and Profits & Losses (Calculations for CFA® and FRM® Exams)

AnalystPrep's Concept Capsules for CFA® and FRM® Exams
This series of video lessons is intended to review the main calculations required in your CFA and FRM exams.

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Options
The buyer of an option has the right but not the obligation to exercise the option. The maximum loss to the buyer is equal to the premium paid for the option. The potential gains are theoretically infinite. To the seller (writer), however, the maximum gain is limited to the premium received after writing the option. The potential loss is unlimited.

In an options contract, two parties transact simultaneously. The buyer of a call or a put option is the long position in the contract while the seller of the option, also known as the writer of the option, is the short position.

Long vs. Short
Here is it important to differentiate between the long and the short party in a contract. The buyer is always said to be long the option. This is quite easy to see for a call option.

However, for a put option, the long position in a put is betting that the underlying price will drop. As such, the long position in a put option is synonymous to being short the underlying.

Expiration
Exchange-traded stock options can either be American or European style. While European options can only be exercised at expiry, American options can be exercised at any point during the life of the option. The actual date of expiry is specified by the exchange.

Strike Prices
Тhe value of the stock directly controls the strike price. At the expiration date, the difference between the stock’s market price and the option’s strike price determines the payoff.

Moneyness
For Call Options:
▪ If the stock price exceeds the exercise price, the option is in-the-money (ITM).
▪ If the stock price is less than the exercise price, the option is out-of-the-money (OTM).
▪ If the current market price is equal to the strike price, the option is at-the-money (ATM).

For Put Options: Just the opposite
▪ If the stock price is less than exercise price, the option is in-the-money (ITM).
▪ If the stock price exceeds the exercise price, the option is out-of-the-money (OTM).
▪ If the current market price is equal to the strike price, the option is at-the-money (ATM).

Intrinsic Value and Time Value
The intrinsic value of an option is the difference between the prevailing market price of the underlying and the strike price.
▪ Intrinsic value of a call option = max(0, St − X)
▪ Intrinsic value of a put option = max(0, X − St)