Forward Commitment and Contingent Claim Features and Instruments

Derivatives

Swaps

Learning Outcome Statement:

define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics

Summary:

Swaps are financial instruments where two parties exchange cash flows based on agreed-upon terms. Typically, one set of cash flows is variable, based on a market reference rate, and the other is fixed. Swaps are used to manage financial risks by altering payment obligations without exchanging the underlying assets. They are similar to forwards in that they have a start and maturity date, but differ as swaps involve multiple exchanges of cash flows over time.

Key Concepts:

Swap Definition

A swap is a contractual agreement to exchange a series of future cash flows between two parties. One party typically pays a fixed rate while the other pays a variable rate tied to an underlying index.

Interest Rate Swap

The most common type of swap, where fixed rate payments are exchanged for payments based on a floating rate. This helps parties manage interest rate exposure.

Swap Mechanics

Involves the exchange of cash flows at specified intervals. The floating rate is reset periodically based on the market reference rate, while the fixed rate remains constant throughout the life of the swap.

Mark-to-Market (MTM)

The value of the swap is recalculated periodically to reflect current market conditions. This can result in a positive or negative MTM, impacting the financial position of the counterparties.

Counterparty Risk

Risk that the other party in the swap agreement will default on their obligations. This risk can be managed through collateral agreements or by transacting through a central counterparty.

Formulas:

Swap Cash Flow Calculation

CF_{\text{net}} = CF_{\text{fixed}} - CF_{\text{floating}}

This formula calculates the net cash flow exchanged in a swap. The fixed and floating payments are netted against one another to determine the payment from one counterparty to the other.

Variables:

$CF_{\text{net}}$ :: Net cash flow exchanged between the parties
$CF_{\text{fixed}}$ :: Cash flow from the fixed rate payer
$CF_{\text{floating}}$ :: Cash flow from the floating rate payer

Units: currency units (e.g., GBP, USD)

Forward Commitments vs. Contingent Claims

Learning Outcome Statement:

contrast forward commitments with contingent claims

Summary:

The learning outcome statement focuses on contrasting forward commitments with contingent claims in financial derivatives. Forward commitments, such as forwards and futures, require both parties to execute the contract at maturity, whereas contingent claims, like options, provide the buyer the right but not the obligation to execute the contract based on the underlying asset's price relative to the exercise price. Both types of derivatives can be structured to create similar market exposures, but they differ significantly in terms of risk and payoff structures.

Key Concepts:

Forward Commitments

Forward commitments are agreements to buy or sell an asset at a predetermined future date for a price agreed upon today. These are binding contracts with symmetrical risk for both the buyer and the seller.

Contingent Claims

Contingent claims are derivatives where the payoff depends on the future price of the underlying asset relative to a predetermined exercise price. Options are a primary example, providing asymmetric risk where the buyer has limited downside with potentially unlimited upside, while the seller has limited upside with potentially unlimited downside.

Comparison of Payoffs

Both forward commitments and contingent claims can be structured to benefit from movements in the underlying asset's price. However, the risk and payoff profiles differ. Forwards have a linear payoff profile, while options allow for protection against adverse movements for a premium.

Formulas:

Forward Profit

ST - F_0(T)

The profit for a long forward position is the difference between the market price at maturity and the forward price agreed upon initially.

Variables:

$ST$ :: price of the underlying asset at maturity
$F_0(T)$ :: forward price agreed upon today for delivery at time T

Units: currency

Call Option Profit

\Pi = \max[0, ST - F_0(T)] - c_0

The profit for a call option is the maximum of zero or the difference between the market price at maturity and the exercise price, minus the premium paid.

Variables:

$ST$ :: price of the underlying asset at maturity
$F_0(T)$ :: exercise price of the option, set equal to the forward price
$c_0$ :: initial premium paid for the call option

Units: currency

Put Option Profit

\Pi = -\max[0, F_0(T) - ST] + p_0

The profit for a short put option is the negative of the maximum of zero or the difference between the exercise price and the market price at maturity, plus the premium received.

Variables:

$ST$ :: price of the underlying asset at maturity
$F_0(T)$ :: exercise price of the option, set equal to the forward price
$p_0$ :: initial premium received for the put option

Units: currency

Futures

Learning Outcome Statement:

Define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics.

Summary:

Futures contracts are standardized forward contracts that trade on exchanges with daily settlement and a central clearing facility ensuring credit guarantee. They involve initial and maintenance margins, and their settlement includes daily mark-to-market adjustments. Futures contracts can be settled by physical delivery or cash, and they require active margin management to maintain the required account balances.

Key Concepts:

Futures Contract

A legally binding agreement to buy or sell a commodity or financial instrument at a predetermined price at a specified time in the future. Unlike forward contracts, futures are standardized and traded on exchanges.

Mark to Market (MTM)

The daily settlement of gains and losses on futures contracts based on the end-of-day settlement price determined by the clearinghouse.

Initial and Maintenance Margin

Initial margin is the funds required to open a futures position, while maintenance margin is the minimum account balance to keep the position open. If the account falls below this level, a margin call is issued requiring the account holder to replenish the margin to the initial level.

Margin Call

A demand for additional capital to be deposited into the margin account to bring it up to the required initial margin level, triggered when the account balance falls below the maintenance margin.

Settlement

The process of resolving the contracts at expiration, either through physical delivery of the asset or cash settlement, based on the difference between the futures price and the spot price at maturity.

Formulas:

Investor Payoff per Barrel

ST - F_0(T)

Calculates the payoff per barrel for the investor, which can be a gain or loss depending on the spot price relative to the agreed forward price.

Variables:

$ST$ :: Spot price at maturity
$F_0(T)$ :: Forward price under the contract

Units: currency per barrel

Total Settlement Amount

N \times (ST - F_0(T))

Calculates the total amount to be paid by the investor to settle the forward contract for N barrels at maturity.

Variables:

$N$ :: Number of barrels
$ST$ :: Spot price at maturity
$F_0(T)$ :: Forward price under the contract

Units: currency

Options

Learning Outcome Statement:

determine the value at expiration and profit from a long or a short position in a call or put option

Summary:

This LOS focuses on understanding the mechanics of options, specifically call and put options, and how to calculate the value at expiration and the resulting profit or loss from either a long or short position. It covers the decision-making process at the option's maturity based on the underlying asset's market price relative to the exercise price, and the financial outcomes of these decisions.

Key Concepts:

Option Mechanics

Options are contingent claims where the buyer has the right but not the obligation to execute the trade at a pre-agreed price (exercise price), and the seller must fulfill the transaction if the buyer chooses to execute. The buyer pays an upfront premium for this right.

Call Option

A call option gives the buyer the right to buy the underlying asset at the exercise price. If the market price at maturity is greater than the exercise price, the buyer can profit by exercising the option. Otherwise, the option is not exercised, leading to a loss equal to the premium paid.

Put Option

A put option gives the buyer the right to sell the underlying asset at the exercise price. The buyer profits if the market price at maturity is less than the exercise price by exercising the option. If not, the loss is limited to the premium paid.

Payoff and Profit Calculation

The payoff for a call option is the difference between the market price and the exercise price if positive; otherwise, it is zero. The profit is the payoff minus the premium paid. For put options, the payoff is the difference between the exercise price and the market price if positive, and profit is calculated similarly.

Formulas:

Call Option Value at Maturity

c_T = \max(0, S_T - X)

This formula calculates the value of a call option at maturity, which is the maximum of zero or the difference between the stock price at maturity and the exercise price.

Variables:

$c_T$ :: value of the call option at maturity
$S_T$ :: stock price at maturity
$X$ :: exercise price

Units: currency

Call Option Buyer's Profit

\Pi = \max(0, S_T - X) - c_0

This formula calculates the profit for the buyer of a call option, which is the call option value at maturity minus the initial premium paid.

Variables:

$\Pi$ :: profit from the call option
$S_T$ :: stock price at maturity
$X$ :: exercise price
$c_0$ :: initial premium paid for the call option

Units: currency

Put Option Value at Maturity

p_T = \max(0, X - S_T)

This formula calculates the value of a put option at maturity, which is the maximum of zero or the difference between the exercise price and the stock price at maturity.

Variables:

$p_T$ :: value of the put option at maturity
$X$ :: exercise price
$S_T$ :: stock price at maturity

Units: currency

Put Option Buyer's Profit

\Pi = \max(0, X - S_T) - p_0

This formula calculates the profit for the buyer of a put option, which is the put option value at maturity minus the initial premium paid.

Variables:

$\Pi$ :: profit from the put option
$X$ :: exercise price
$S_T$ :: stock price at maturity
$p_0$ :: initial premium paid for the put option

Units: currency

Forwards, Futures, and Swaps

Learning Outcome Statement:

define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics

Summary:

This LOS focuses on defining and comparing the basic characteristics of various derivative instruments including forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives. These instruments are essential for financial markets as they allow for risk management and speculative opportunities. The content covers the structure, payoff profiles, and specific features of each type of derivative.

Key Concepts:

Forward Contracts

Forward contracts are over-the-counter derivatives where two parties agree to buy or sell an asset at a predetermined future date and price. They are customizable but involve higher counterparty risk.

Futures Contracts

Futures contracts are similar to forwards but are standardized and traded on exchanges, which provides higher liquidity and lower default risk due to the presence of a clearinghouse.

Swaps

Swaps involve the exchange of one set of cash flows for another. Though not detailed in the provided content, they typically involve interest rates, currencies, or commodities.

Options

Options give the holder the right, but not the obligation, to buy or sell an asset at a set price before a certain date. Calls and puts allow for strategies based on directional bets on asset prices.

Credit Derivatives

Credit derivatives are financial tools used to manage exposure to credit risk, primarily through instruments like credit default swaps (CDS), which provide insurance against default events.

Formulas:

Forward Contract Payoff

P = S_T - F_0(T)

This formula calculates the payoff for the buyer of a forward contract at maturity. The payoff is positive if the spot price at maturity exceeds the pre-agreed forward price.

Variables:

$P$ :: Payoff of the forward contract
$S_T$ :: Spot price of the underlying asset at maturity
$F_0(T)$ :: Pre-agreed forward price of the asset for delivery at time T

Units: Currency (e.g., USD)

Credit Derivatives

Learning Outcome Statement:

Define forward contracts, futures contracts, swaps, options (calls and puts), and credit derivatives and compare their basic characteristics.

Summary:

Credit derivatives are financial instruments that derive their value from the credit risk associated with an underlying entity, which could be a single issuer or a collection of issuers. The most common form of credit derivative is the Credit Default Swap (CDS), which allows investors to manage potential losses from issuer defaults separately from owning the underlying bond. CDS contracts involve payments based on credit events related to the underlying issuer and are priced based on credit spreads, reflecting the probability of default and loss given default.

Key Concepts:

Credit Default Swap (CDS)

A CDS is a financial derivative that allows an investor to swap or offset their credit risk with that of another investor. For example, a credit protection buyer pays a periodic fee to a protection seller who in return will pay the buyer if a credit event (like default) occurs, based on the notional amount of the contract.

Credit Event

A credit event in a CDS contract is a trigger that causes the protection seller to make a payment to the protection buyer. Common credit events include bankruptcy, failure to pay, and restructuring of debt.

Credit Spread

This is the spread between the yield on a corporate bond and a comparable maturity government bond. In CDS, the credit spread reflects the risk of default and the loss given default. A higher spread indicates higher risk.

Loss Given Default (LGD)

LGD is the percentage of the total exposure that is lost if a borrower defaults, after recovery from collateral and other mitigating factors. It is used in the calculation of potential payments under a CDS contract.

Formulas:

CDS Payment Calculation

\text{Payment} = \text{LGD} \% \times \text{Notional}

This formula calculates the payment that the protection seller must make to the protection buyer in the event of a credit event, based on the notional amount of the contract and the agreed upon percentage of loss given default.

Variables:

$LGD$ :: Loss Given Default as a percentage
$Notional$ :: The total amount of the underlying asset on which the CDS contract is based

Units: currency

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