We now move to the other major category of derivative instruments called contingent claims. The holder of a contingent claim has the right, but not the obligation to make a final payment contingent on the performance of the underlying.
In a contingent claim, two parties, A and B, sign a contract at time 0 to engage in a transaction at time T. Unlike a forward or futures contract, A has the right, but not the obligation to make a payment and take delivery of the asset at time T.
There are three types of contingent claims: options, credit derivatives, and asset-backed securities.
An option is a derivative contract in which one party, the buyer, pays a sum of money to the other party, the seller or writer, and receives the right to either buy or sell an underlying asset at a fixed price either on a specific expiration date or at any time prior to the expiration date. Options trade on exchanges, or they can be customized in the OTC market.
The buyer/holder of an option is said to be long.
The seller/writer of an option is said to be short.
There are two types of options based on when they can be exercised:
There are two types of options based on the purpose it serves:
Assume there are two parties: A and B. A is the seller, writer, or the short party. B is the buyer or the long party. A and B sign a contract, according to which B has the right to buy one share of Strong Steel Inc. for $50 after six months.
In our example, B has bought the right to buy, which is called a call option. The right to sell is called a put option. If B has the right to buy a share (exercise the option) of Strong Steel Inc. anytime between now and six months, then it is an American-style option. But if he can exercise the right only at expiration, then it is a European-style option. $50, the price fixed at which the underlying share can be purchased, was fixed at inception and is called the strike price or exercise price.
B bought the right to buy the share at expiration from A. So B has to pay A, a sum of money called the option premium for holding this right without an obligation to purchase the share.
The call premium B paid is $3. An investor would buy a call option if he believes the value of the underlying would increase.
The diagram below shows the call option payoff and profit for both a buyers and sellers perceptive.
Call option buyer and seller payoff at expiration:
cT = Max (0,ST – X)
ST = stock’s price
X = exercise price
For example, suppose you buy a call option with an exercise price of 30 and an expiration of three months for a premium of 1.00 when the stock is trading at 25. At expiration, consider the outcomes when the stock’s price is 25, 30, or 35. The buyer’s payoffs would be:
For ST = 25, payoff = cT = Max(0,ST – X) = Max(0,25 – 30) = Max(0, –5) = 0.
For ST = 30, payoff = cT = Max(0,ST – X) = Max(0,30 – 30) = Max(0, 0) = 0.
For ST = 35, payoff = cT = Max(0,ST – X) = Max(0,35 – 30) = Max(0, 5) = 5.
To the seller, who received the premium at the start, the payoff is:
–cT = –Max(0,ST – X)
At expiration, the call seller’s payoffs are:
For ST = 35, payoff = –cT = –Max(0,ST – X) = –Max(0,35 – 30) = 0.
For ST = 30, payoff = –cT = –Max(0,ST – X) = –Max(0,30 – 30) = 0.
For ST = 35, payoff = –cT = –Max(0,ST – X) = –Max(0,35 – 30) = –5.
The call buyer’s profit would be:
Profit = Max(0,ST – X) – c0
c0 = option premium
For ST = 25, profit = Max(0,ST – X) – c0 = Max(0,25 – 30) – 1.00 = – 1.
For ST = 30, profit = Max(0,ST – X) – c0 = Max(0,30 – 30) – 1.00 = – 1.00.
For ST = 35, profit = Max(0,ST – X) – c0 = Max(0,35 – 30) – 1.00 = 4.00.
The call seller’s profit is:
Π = –Max(0,ST – X) + c0
At expiration, the call seller’s profit for each underlying price at expiration are:
For ST = 35, profit = –Max(0,ST – X) + c0 = –Max(0,35 – 30) + 1.00 = 1.00.
For ST = 30, profit = –Max(0,ST – X) + c0 = –Max(0,30 – 30) + 1.00 = 1.00.
For ST = 35, profit = –Max(0,ST – X) + c0 = –Max(0,35 – 30) + 1.00 = –4.00.
Put option buyer and seller payoff at expiration:
An investor would buy a put option if he believes the value of the underlying would decrease. If it decreases by expiration date, the investor has a right to exercise the option to sell the underlying at the exercise price, which will be greater than the then market price.
The payoff to the put holder is:
pT = Max(0,X – ST)
The put buyer’s profit would be:
Π = Max(0,X – ST) – p0
where: p0 is option premium.
The payoff for the seller is:
–pT = –Max(0,X – ST)
The put seller’s profit would be:
Π = –Max(0,X – ST) + p0
A credit derivative is a class of derivative contracts between two parties, a credit protection buyer and a credit protection seller, in which the latter provides protection to the former against a specific credit loss. The main type of credit derivative is a credit default swap.
Credit Default Swap
A credit default swap is a derivative contract between two parties, a credit protection buyer and a credit protection seller, in which the buyer makes a series of cash payments to the seller and receives a promise of compensation for credit losses resulting from the default of a third party.
An asset-backed security is a derivative contract in which a portfolio of debt instruments is assembled and claims are issued on the portfolio in the form of tranches, such that the prepayments or credit losses are allocated to the most junior tranches first and the most senior tranches last.
The following exhibit shows how asset-backed securities are created.
Listed below are the major points related to asset-backed securities:
Hybrid instruments combine derivatives, fixed-income securities, currencies, equities, and commodities. An example of a hybrid is a callable bond or a convertible bond that is created by combining bonds and options.
We have seen that derivatives are contracts that derive their value from an underlying. The commonly used underlyings are listed below: