Payoffs of Derivative Contracts
We will cover following topics
Option Contract Payoffs
Options contracts are financial derivatives that provide the buyer with the right, but not the obligation, to buy (call option) or sell (put option) an underlying asset at a predetermined price (strike price) on or before a specified expiration date. The payoff of an option contract depends on the market price of the underlying asset at expiration.
Call Option
The payoff for a call option depends on whether the market price of the underlying asset (S) at expiration is greater than the strike price (K). The call option payoff (C) can be calculated as follows:
$$\text{Put Option Payoff (P)} = Max(S - K, 0)$$
If the market price (S) is higher than the strike price (K), the call option is “in-the-money,” and the payoff is the difference between the market price and the strike price. If the market price is lower than the strike price, the call option is “out-of-the-money,” and the payoff is zero.
Example: Let’s consider a call option with a strike price of 50 USD. If the market price of the underlying asset at expiration is 60 USD, the call option payoff will be Max(60 - 50, 0) = 10 USD.
Put Option
The payoff for a put option depends on whether the market price of the underlying asset (S) at expiration is less than the strike price (K). The put option payoff (P) can be calculated as follows:
$$\text{Put Option Payoff (P)} = Max(K - S, 0)$$
If the market price (S) is lower than the strike price (K), the put option is “in-the-money,” and the payoff is the difference between the strike price and the market price. If the market price is higher than the strike price, the put option is “out-of-the-money,” and the payoff is zero.
Example: Consider a put option with a strike price of 80 USD. If the market price of the underlying asset at expiration is 70 USD, the put option payoff will be Max(80 - 70, 0) = 10 USD.
Forward Contract Payoffs
Forward contracts are agreements between two parties to buy or sell an asset at a specified price (the forward price) on a future date. Unlike options, forward contracts have an obligation to execute the trade at the agreed-upon price. The payoff of a forward contract is based on the difference between the spot price (current market price) of the underlying asset at expiration and the forward price.
Long Forward
The payoff for the party (buyer) that enters into a long forward contract (agrees to buy the asset) can be calculated as follows:
$$\text{Long Forward Payoff} = S - F $$
where $S$ is the spot price at expiration and $F$ is the forward price agreed upon in the contract. If the spot price is higher than the forward price, the long forward contract results in a positive payoff.
Example: Suppose a party enters into a long forward contract to buy one share of a stock at 100 USD after three months, and the spot price at expiration is 120 USD. The long forward payoff will be: 120 - 100 = 20 USD.
Short Forward
The payoff for the party (seller) that enters into a short forward contract (agrees to sell the asset) can be calculated as follows:
$$\text{Long Forward Payoff} = F - S $$
If the spot price at expiration is higher than the forward price, the short forward contract results in a negative payoff.
Example: Let’s consider a party that enters into a short forward contract to sell one share of a stock at 90 USD after six months, and the spot price at expiration is 100 USD. The short forward payoff will be: 90 - 100 = -10 USD.
Conclusion
Understanding the payoffs of derivative contracts is crucial for investors and traders to make informed decisions. Options contracts offer flexibility, allowing investors to participate in price movements without the obligation to buy or sell. The payoffs of call and put options depend on the relative prices of the underlying asset and the strike price at expiration. On the other hand, forward contracts involve an obligation to buy or sell the asset at a predetermined price on a future date, and their payoffs are determined by the difference between the spot price and the forward price. By comprehending these payoffs, market participants can assess risk exposures and design strategies that align with their financial goals and risk tolerance.