There are two general classes of derivatives: forwards and contingent claims. Forward commitments are legal agreements for the two parties to transact in the future at a previously agreed-on price. The various types of forward commitments are called forward contracts, futures contracts, and swaps.
Contingent claims give the holder the right but not the obligation to buy or sell the underlying at a pre-determined price. The primary contingent claim is called an option. Others include credit default swaps and asset-backed securities.
A forward contract is an over-the-counter derivative contract in which two parties agree that one party, the buyer, will purchase an underlying asset from the other party, the seller, at a later date at a fixed price they agree on when the contract is signed
Characteristics of a forward contract include:
The party getting into the contract to sell is called short party and one promising to buy is called long party.
When the underlying asset’s price goes up, the long party gains (since forward price is fixed) while the short party loses (since he could have sold at the higher market price).
PAYOFF FROM A FORWARD CONTRACT
Assume that a buyer has entered into a forward contract with a seller for a price of F0(T), with delivery of one unit of the underlying asset to occur at time T. At time T, the price of the underlying is ST. The long is obligated to pay F0(T), for which he receives an asset worth ST. If ST > F0(T), it is clear that the transaction has worked out well for the long. He paid F0(T) and receives something of greater value. Thus, the contract effectively pays off ST ‒ F0(T) to the long, which is the value of the contract at expiration. The short has the mirror image of the long.
Assumptions and Symbol definitions:
The long party agrees to buy at the forward price, and the short party agrees to sell at the forward price.
Except in the extremely rare event that the underlying price at T equals the forward price, one party will pay the other
Example: Forward Payoff
Barbara Nix agrees to buy 1 kilogram of gold in 90 days at a price of $38,000 from PM Metals Inc (short party). After 90 days, the spot price of gold is $38,500 per kilo.
Required: Payoffs of both long party and short party.
Solution:
F0(T) = $38,000/kilo
ST = $38,500/kilo
Payoff to the long party (Nix) at expiration (T)
= ST ‒ F0(T) = $38,500 ‒ $38,000 = $500
Payoff to the short party at expiration (T) = ‒$500
Forward contracts need not specifically settle by delivery of the underlying asset. They can settle by an exchange of cash. These contracts—called non-deliverable forwards (NDFs), cash-settled forwards, or contracts for differences—have the same economic effect as do their delivery-based counterparts. For example, for a physical delivery contract, if the long pays F0(T) and receives an asset worth ST, the contract is worth ST – F0(T) to the long at expiration. A non-deliverable forward contract would require the short to simply pay cash to the long in the amount of ST – F0(T).
A futures contract is a standardized derivative contract created and traded on a futures exchange in which two parties agree that one party, the buyer, will purchase an underlying asset from the other party, the seller, at a later date and at a price agreed on by the two parties when the contract is initiated and in which there is a daily settling of gains and losses and a credit guarantee by the futures exchange through its clearinghouse.
A fixed price at which the underlying will be exchanged is set by the buyer and seller when the contract is initiated. This agreed-upon price is called the futures price.
Futures contracts have specific underlying assets, times to expiration, delivery and settlement conditions, and quantities. The exchange offers a facility in the form of a physical location and/or an electronic system as well as liquidity provided by authorized market makers.
Some futures contracts contain a provision limiting price changes (price limits), setting a band relative to the previous day’s settlement price, within which all trades must occur. If market participants wish to trade at a price above the upper band, trading stops, which is called limit up, until two parties agree on a trade at a price lower than the upper limit. Likewise, if market participants wish to trade at a price below the lower band, which is called limit down, no trade can take place until two parties agree to trade at a price above the lower limit.
Futures contracts are marked to market in a process called daily settlement.
Differences between forwards and futures contracts
| Basis | Forwards | Futures |
| Primary Market | Dealers | Organized Exchange |
| Secondary Market | None | The Primary Market |
| Contracts | Negotiated | Standardized |
| Delivery | Contracts expire | Rare delivery |
| Collateral | None | Initial Margin, mark-the- market |
| Credit Risk | Depends on Parties | None (Clearing House) |
| Market Participants | Large Firms | Wide Variety |
A swap is an over-the-counter derivative contract in which two parties agree to exchange a series of cash flows whereby one party pays a variable series that will be determined by an underlying asset or rate and the other party pays either (1) a variable series determined by a different underlying asset or rate or (2) a fixed series.
The most common swap is the fixed-for-floating interest rate swap. In fact, this type of swap is so common that it is often called a “plain vanilla” swap. A fixed-for-floating interest rate swap or plain Vanilla Swap may be used to convert a floating rate loan to a fixed rate loan.
A swap is similar to a forward contract in the following ways:
However, a Swap is used to hedge multi-period risk, whereas a forward contract hedges only single-period risks, thus a swap can be viewed as a series of forward rate agreements (FRAs), while a forward contract is a one-period swap.
Example:
Company A borrows $50,000,000 for 2 years with quarterly interest payments made at 90-day Libor. The firm is worried that Libor (a floating rate) may increase.
Company A enters into a 2-year fixed-for-floating swap with Swap Dealer B based on a 30/360 day count convention and a notional principal of $50,000,000. Company A agrees to make quarterly payments based on a fixed rate of 4.5% in exchange for a payment from Dealer B based on 90-day Libor.
If Libor sets at 6% at the end of a quarter, Company A will receive a payment based on the net difference of 1.5% i.e. 50,000,000 x (1.5%-4.5%) x (90/360). Company A will pay 6% and get 1.5% from their counterparty, resulting in a net payment of 4.5%.
If Libor sets at 3.5% at the end of a quarter, Company A will make a payment to Swap Dealer B based on a net difference of 1%. Company A would have paid 3.5% + 1% to Swap dealer B, making A’s rate effectively 4.5%.
In either case, by entering the swap, Company A has effectively converted a floating-rate loan based on Libor into a 4.5% fixed rate loan.
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.
When an option is terminated, either early or at expiration, the holder of the option chooses whether to exercise it. If he/she exercises it, he/she either buys or sells the underlying asset, but he/she does not have both rights. The buyer pays the option writer a sum of money called the option premium, or just the “premium.” It represents a fair price for the option, and in a well-functioning market, it would be the value of the option.
The right to buy is one type of option, referred to as a call or call option, whereas the right to sell is another type of option, referred to as a put or put option.
Put and call options may be American style, European style or Bermuda style. American-style options are exercisable early (any time before expiration) or at expiration. Options that can be exercised only at expiration are referred to as European-style. Bermuda-style options are exercisable on specified times before expiration date.
It is extremely important that you do not associate these terms with where these options are traded. Both types of options trade on most continents.
Option Payoffs
An option’s outcome or payoff is dependent on the outcome or payoff of an underlying asset. The max statement, which takes the greater of 0 and ST – X for the call or 0 and X-ST for the put, tells us the payoff from the option can never be less than 0.
Payoff to the call buyer: cT = Max(0,ST – X)
Payoff to the put buyer: pT = Max(0,X – ST)
Where: ST: the price of the underlying at the expiration date,T
X: the exercise price of the option.
Example: Option Payoff
At expiration the underlying asset price ST is $28. If the strike price X is $25, what is the payoff of the put and call?
Solution:
Payoff to the call buyer:
cT = Max(0,ST – X) = Max(0,$28 – $25) = $3
Payoff to the put buyer:
pT = Max(0,X – ST) = Max(0,$25 – $28) = 0
When the option has a positive payoff it is said to be in the money. In the example above, the call option is in the money. The put option is out of the money because X – ST is less than 0. When ST = X, the option is said to be at the money.
Option Profit
Since option buyer must pay a price (or option premium), the profit is computed by subtracting the option premium from the option payoff.
Profit to the call buyer: Π = Max(0,ST – X) – c0
Profit to the put buyer: Π = Max(0,X – ST) – p0
Where:
ST: the price of the underlying at the expiration date, T, and
X: the exercise price of the option
c0: the price (premium) of the call option
p0: the price (premium) of the put option
Example: Option Profit
A put and call on CBX stock both have a strike price X = $30. The call initially costs $1, and the put costs $2.
What is the profit on the call and put if the price of CBX stock at expiration (ST) is $27.50?
Solution:
Profit to the call buyer: Π = Max(0,ST – X) – c0 =
Max(0,$27.50 – $30) – $1 = – $1
Profit to the put buyer: Π = Max(0,X – ST) – p0 =
Max(0,$30 – $27.50) – $2 = $0.50
Options cost money. Since the payoff can never be less than 0, the loss for the buyer of a call or put is limited to the premium paid. In this case, the call buyer lost $1, because the call expired out of the money. The put had a payoff of $2.50, but cost $2, resulting in a profit of $0.50.
A credit derivative is a class of derivative contracts between two parties, a protection buyer and a credit protection seller, which the latter provides protection to the former against a specific credit loss.
There are several types of credit derivatives:
Credit default swap is the main component of this class of derivatives. Credit default swap is a 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, which have different priorities of claims on the payments made by the debt securities such that prepayments or credit losses are allocated to the most-senior tranches last.
Since these securities are based on the underlying instruments such as mortgages, they can be classified as derivatives
These securities are discussed in more details under the alternatives investments analysis paper.
Hybrid derivatives combine derivatives, fixed-income securities, currencies, equities and commodities. For example, combining an option with bonds to form a callable bond or a convertible bond.
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