derivatives 2: Forward Commitment and Contingent Claim Features and Instruments

What is a firm commitment derivative?

• Both parties are obligated to perform

• No optionality (unlike options)

e.g forwards, futures swaps

4 Common features of forwards, futures, and swaps?

• Fixed contract size

• Defined underlying

• Pre-agreed price

• Future exchange of cash flows or assets

What is a forward contract?

An OTC agreement to buy or sell an underlying at a fixed price on a future date.

4 key features of forwards contracts

• Traded OTC (over-the-counter)

• Highly customizable

• No initial cash exchange (typically)

• Settled at maturity

What is the forward buyer’s payoff formula and who makes profit when?

$$S_{T}-F_0\left(T\right)$$

$S_T =$ spot price

$F_0(T) =$ forward price

• buyer profit when spot price > forward price

• seller profit when spot price < forward price

Why are forwards called linear derivatives?

Because payoff changes linearly with the underlying price.

What is unique about forward contracts at initiation (t=0)?

No upfront payment is exchanged.

What is a futures contract?

A standardised forward contract traded on an exchange.

What is standardised in a futures contract?

• Contract size

• Maturity dates

• Underlying quality/specification

• Settlement procedure

what features do futures have from being exchange traded?

• More liquid than forwards

• More transparent pricing

• Greater protection from loss

Explain the long futures and short futures positions

Long Futures Position

• Buyer agrees to buy underlying later

• Benefits if price rises

Short Futures Position

• Seller agrees to sell underlying later

• Benefits if price falls

What is the futures price notation?

$$f_0(T)$$

What is mark to market (MTM)?

At the end of every trading day:

• Gains/losses are settled immediately

• Contracts are repriced to current settlement price

• performed by clearing house

purpose of MTM

• Reduces counterparty risk

• Prevents large unpaid losses from accumulating

how do margins work?

1. deposit inital margin in a futures margin account

2. clearing house uses this to settle daily MTM

3. must have a minimum balance called a maintenance margin

4. if Margin Balance < Maintenance Margin a margin call occurs

5. must top up to initial margin → this amount is called variation margin

6. if they can’t → close contract immediately and payout any losses

What are price limits?

Exchange-imposed maximum daily price movement bands

• trading may halt if limit is reached

What is a circuit breaker?

Temporary pause in trading during extreme volatility.

Role of the clearinghouse?

The clearinghouse:

• Guarantees contract performance

• Collects margins

• Transfers gains/losses daily

• Reduces default risk

If trader defaults:

• Clearinghouse covers obligations using insurance fund

futures payoff formula

$$S_T - f_0(T)$$

What is open interest?

Number of outstanding futures contracts.

settled at maturity through cash or physical delivery

How can traders close futures positions before expiration?

Enter an offsetting trade.

forwards vs futures

1. market

2. customisation

3. credit risk

4. settlement

5. liquidity

Feature	Forwards	Futures
Market	OTC	Exchange-traded
Customisation	High	Low
Credit risk	Higher	Lower (clearinghouse)
Settlement	At maturity	Daily mark-to-market
Liquidity	Lower	Higher

What is a swap?

a firm commitment in which two counterparties exchange a series of future cash flows.

what are the two common cash flow streams in a swap?

Fixed-Rate Payer

• Pays fixed interest

• Receives floating interest

Floating-Rate Payer

• Pays floating interest

• Receives fixed interest

What type of swap is most common?

In an interest rate swap:

• One party pays a fixed interest rate - swap rate stays constant

• The other pays a floating market reference rate (MRR) - MRR resets each period

How are swaps similar to forward contracts?

• negotiated OTC contracts

• start date

• maturity date

• underlying specified by counterparties.

How can a swap be viewed conceptually in reference to forwards?

As a series of forward exchanges occurring over time.

are swap payments usually exchanged gross or net?

• Only the difference between payments is exchanged

• Not the full gross amounts

reduces:

• Transaction costs

• Cash movement

What is the notional principal in a swap?

• reference amount used to calculate interest payments

• usually not exchanged.

why might investors use swaps?

Use swaps to:

• Increase/decrease duration

• Change portfolio exposure without trading bonds

why might issuers use swaps?

• Convert fixed debt to floating debt

• Convert floating debt to fixed debt

How are expected floating-leg cash flows estimated in a swap?

Using forward market reference rates derived from spot rates.

How is the swap fixed rate determined?

fixed yield that equates the present value of fixed and floating payments.

Swap vs vs forward vs futures

1. payment frequency

2. market

3. standardised?

4. coiunterparty risk?

5. flexibility

Feature	Swap	Forward	Futures
Payments	Multiple	One	Daily MTM
Market	OTC	OTC	Exchange
Standardized	No	No	Yes
Counterparty risk	Moderate/High	High	Low
Flexibility	High	High	Lower

What is a contingent claim?

A derivative contract in which one counterparty has the right to decide whether the trade will settle based on the underlying value.

what is an call option

It gives the buyer:

• a right

• but not an obligation to exercise in the future at pre agreed price

The seller:

• has the obligation to fulfill the contract if exercised.

what is the option premium?

An amount that is paid upfront from the option buyer to the option seller. Reflects the value of the option buyer’s right to exercise in the future.

What is a put option?

The right to sell an underlying asset at a specified exercise price.

European vs american options

European: only exercised at maturity

American: Can be exercised whenever

what is an options intrinsic value?

The amount gained (per unit) by an option buyer if an option is exercised at any given point in time.

AKA the exercise value

What is the payoff formula for a long put?

$$p_{T}=\max\left(0,X-S_{T}\right)$$

$X =$ pre agreed purchase price

$S_T =$ stock price at time T

What is the profit formula for a long put?

$$\Pi=\max\left(0,X-S_{T}\right)-p_0$$

$X =$ pre agreed purchase price

$S_T =$ stock price at time T

$p_0=$ put premium

long put

1. benefits when

2. max gain

3. max loss

Feature	Result
Benefits when	Price falls
Maximum gain	$$X - p_0$$
Maximum loss	Premium paid

long put

1. benefits when

2. max gain

3. max loss

Feature	Result
Benefits when	Price raises or stays high
Maximum gain	Premium received
Maximum loss	Large but limited

What is the payoff formula for a long call?

$$p_{T}=\max\left(0,S_{T}-X\right)$$

$X =$ pre agreed purchase price

$S_T =$ stock price at time T

What is the profit formula for a long call?

$$\Pi=\max\left(0,S_{T}-X\right)-c_0$$

$X =$ pre agreed purchase price

$S_T =$ stock price at time T

$c_0=$ option premium

Condition for

1. In the money

2. at the money

3. out of the money

Type	Condition
In-the-money	S_t > X
At-the-money	$$S_t = X$$
Out-of-the-money	S_t < X

for a long option what is

1. max loss

2. max gain

3. break even

Feature	Result
Maximum loss	Premium paid
Maximum gain	Unlimited
Breakeven	$$X + c_0$$

short call

1. benefits when

2. max gain

3. max loss

Feature	Result
Benefits when	Price falls or stays low
Maximum gain	Premium received
Maximum loss	Unlimited

Why is there time value in options?

Before maturity:

• More time = greater chance of profit

• Therefore option has additional time value

• As maturity approaches time value → 0

What is a credit derivative?

A derivative contract based on the credit risk or default risk of a debt issuer or group of issuers.

what is a credit default swap (CDS)

A CDS allows one party to:

• transfer credit risk

• without transferring ownership of the bond.

What determines CDS credit spreads?

• Probability of default (POD)

• loss given default (LGD).

What is the relationship between credit spreads and bond prices?

higher credit spreads correspond to lower bond prices.

What features do CSD share with firm commitments

CDS are contingent claims

• Exercise timing and payout depend on credit events, not investor choice

  • Unlike options

• A CDS priced at par spread has zero NPV

  • like interest rate swaps

• Notional amount is not exchanged

  • Used only for calculating payments/settlement

how does CDS work for Protection buyer

Protection Buyer

• Pays fixed premium

• Receives payout if default occurs

How does a CDS work for protection seller

• Receives premiums

• Pays if credit event occurs

• Exposed to default risk

• Similar to holding the bond (long credit risk)

what is a credit event?

A CDS only pays out if something bad happens to the borrower, such as:

• Bankruptcy

• Failure to pay debt

• Debt restructuring (forced change in repayment terms)

CDS payout formula

CDS payout = Loss Given Default (LGD) × Notional

CDS for hedging

This is like insurance on a bond

• You already own a bond from a company

• You worry it might default

• You buy CDS protection

If default happens:

• You lose money on the bond

• You gain money from CDS
  → Loss is offset

CDS for speculation

Short credit risk position (you benefit when credit quality worsens)

• You do NOT own the bond

• You still buy CDS

Why?

• You think the company will become riskier

• Or bond prices will fall (credit spreads widen)

If that happens:

• CDS value increases
  → You profit