Chapter 8 - Over-the-Counter Options

Question 1

What is an Asian option?

Answer 1

An option whose payoff is based on
the average price of the underlying
asset over time until expiration. Also
known as an average price option.

Question 2

What is a barrier option?

Answer 2

An option where the payoff depends
on whether or not the underlying asset
reaches a pre-defined barrier during
the life of the option.

Question 3

What is a caplet?

Answer 3

The individual option components of
an interest rate cap.

Question 4

What is a ceiling rate?

Answer 4

The dealer and the customer enter into
an agreement in which they specify the term for the cap, the reference rate, the exercise rate (known as the ceiling
rate), the cap’s principal, and the settlement dates. For example, the term could be two years, five years, or more,
and the reference rate could be the 3-month term Secured Overnight Financing Rate (SOFR), the 6-month=term
SOFR, or the 3-month Treasury bill.

Question 5

What is a compound option?

Answer 5

An option on an option.

Question 6

What is an exotic option?

Answer 6

Any option that is not traded on
an exchange and is not essentially
identical to one traded on an exchange.

Question 7

What is a floor rate?

Answer 7

An interest rate floor is a multi-period interest rate option identical to a cap, except that the floor writer pays the
floor purchaser when the reference rate drops below the contract rate, which is called the floor rate.

Question 8

What is an interest rate cap?

Answer 8

Essentially a series of European call
options on interest rates (as opposed
to call options on an underlying debt
instrument). The holder of the cap
gets paid on each settlement date the
amount, if any, by which the reference
interest rate is above the exercise or
strike price.

Question 9

What is an interest rate collar?

Answer 9

A combination of a cap and a floor
created by purchasing a cap, while
simultaneously selling a floor.

Question 10

What is an interest rate floor?

Answer 10

Essentially a series of European put
options on interest rates (as opposed
to put options on an underlying debt
instrument). The holder of the floor
gets paid on each settlement date the
amount, if any, by which the reference
interest rate is below the exercise or
strike price.

Question 11

What is a multi-asset option?

Answer 11

Consists of a family of options whose
payoffs depend on the prices of more
than one asset.

Question 12

What is a shout option?

Answer 12

An option that permits the holder at
any time during the life of the option
to establish a minimum payoff that
will occur at expiration.

Question 13

Describe what interest rate caps, floors and collars are.

Answer 13

Interest Rate Caps

An interest rate cap sets an upper limit on the interest rate that a borrower has to pay on a variable rate loan. If the market interest rate exceeds this cap, the borrower only pays the capped rate. This provides protection against rising interest rates.

Example:

Loan Details: A borrower takes a $100,000 variable rate loan with a cap of 5%.
Scenario: If the market interest rate rises to 6%, the borrower will only pay 5% due to the cap.

Interest Rate Floors

An interest rate floor sets a lower limit on the interest rate that a lender will receive on a variable rate loan. If the market interest rate falls below this floor, the lender still receives the floor rate. This provides protection against falling interest rates.

Example:

Loan Details: A lender provides a $100,000 variable rate loan with a floor of 3%.
Scenario: If the market interest rate drops to 2%, the lender will still receive 3% due to the floor.

Interest Rate Collars

An interest rate collar combines both a cap and a floor, setting both upper and lower limits on the interest rate. This creates a range within which the interest rate can fluctuate. Borrowers and lenders use collars to ensure that the interest rate stays within a manageable range, providing protection against both high and low rate extremes.

Example:

Loan Details: A borrower takes a $100,000 variable rate loan with a cap of 5% and a floor of 3%.
Scenario:
    If the market interest rate rises to 6%, the borrower pays 5% due to the cap.
    If the market interest rate falls to 2%, the borrower pays 3% due to the floor.
    If the market interest rate stays within 3% to 5%, the borrower pays the market rate.

Question 14

Explain how interest rate caps, floors and collars can be used to hedge interest rate risk.

Answer 14

• Interest Rate Caps
  An interest rate cap is a series of European-style OTC interest rate call options that mature on dates
  established by the two counterparties. Interest rate caps establish a maximum interest rate that will be paid
  by the holder of the cap for the term of the contract. The individual options within an interest rate cap are
  referred to as caplets.
  An issuer of floating-rate debt, or any party that is at risk that a floating interest rate will rise, can purchase an
  interest rate cap to set the maximum interest rate that the issuer will pay on the debt in a rising interest rate
  environment.
• Interest Rate Floors
  An interest rate floor is a series of European-style OTC interest rate put options that mature on dates
  established by the two counterparties. Interest rate floors establish a minimum interest rate that will be
  received by the holder of the floor for the term of the contract.
  Any party that is at risk that a floating interest rate will fall can purchase an interest rate floor to set the
  minimum rate to be received in a declining interest rate environment.
• Interest Rate Collars
  An interest rate collar is a combination of a cap and a floor in which the purchaser of the collar buys a cap and
  simultaneously sells a floor. The seller of the collar is on the other side of the transaction: selling the cap and
  buying the floor.
  An interest rate collar can be purchased by an issuer of floating-rate debt who wants to cap the maximum
  interest rate on the loan, but finds the cost of an interest rate cap too expensive. To effectively reduce the cost
  of the cap, an out-of-the-money interest rate floor can be sold, and the proceeds can be applied against the
  cost of the cap.

Question 15

Calculate the payoffs from interest rate caps, floors and collars given all the inputs.

Answer 15

The buyer of an interest rate cap will receive a payoff from the writer of the cap at the end of an interest
payment period if the reference rate was above the ceiling rate at the beginning of the interest payment period.
The payoff is calculated as follows:

Payoff = (Reference Rate − Ceiling Rate) × Principal × Length of the Payment Period

The buyer of an interest rate floor will receive a payoff from the writer of the floor at the end of an interest
payment period if the reference rate is below the floor rate at the beginning of the interest payment period.
The payoff is calculated as follows:

Payoff = (Floor Rate − Reference Rate) × Principal × Length of the Payment Period

The buyer of a collar will receive payments from the cap when the reference rate is above the ceiling rate, but
will be required to make payments on the floor when the reference rate is below the floor rate.

Question 16

List and describe the main features of exotic options.

Answer 16

• Compound options are options on options.
• Asian options are options whose payoffs are based on the average price of the underlying security during the
  term of the contract.
• Barrier options are options whose payoffs depend on whether or not the underlying asset reaches a
  predetermined “barrier” price during the life of the option.
• Multi-asset options are options whose payoffs depend on the prices of more than one asset.
• Shout options are options that permit the holder at any time during the life of the option to establish,
  on his/her choice, a minimum payoff that will occur at expiration.

Question 17

Describe what compound options, asian options, barrier options, multi-asset options, and shout options are.

Answer 17

Compound Options

Compound options are options on options. They give the holder the right, but not the obligation, to buy (or sell) another option at a specified price before the compound option’s expiration. There are two main types of compound options:

Call on a Call (CoC): The right to buy a call option.
Put on a Call (PoC): The right to sell a call option.
Call on a Put (CoP): The right to buy a put option.
Put on a Put (PoP): The right to sell a put option.

Example:

Scenario: A company might use a CoC to defer the decision to purchase an option on a project until more information is available.

Asian Options

Asian options are a type of option where the payoff depends on the average price of the underlying asset over a certain period, rather than just its price at maturity. There are two main types:

Average Price Options: Payoff is based on the difference between the average price of the underlying asset over the period and the strike price.
Average Strike Options: The strike price is the average price of the underlying asset over the period.

Example:

Scenario: An investor buys an Asian call option with a strike price of $50, and the average price of the underlying asset over the option's life is $55. The payoff is based on this average price.

Barrier Options

Barrier options are options where the payoff depends on whether the underlying asset’s price reaches a certain level (the barrier) during the option’s life. There are several types:

Knock-In Options: Become active only if the underlying asset's price reaches the barrier.
Knock-Out Options: Become inactive if the underlying asset's price reaches the barrier.

Example:

Scenario: A knock-in call option with a strike price of $100 and a barrier at $110 only becomes exercisable if the asset's price hits $110.

Multi-Asset Options

Multi-asset options (or rainbow options) depend on the performance of two or more underlying assets. The payoff can be based on various combinations of the assets’ prices.

Example:

Scenario: An option on the average performance of a basket of stocks from different sectors, where the payoff is determined by the combined performance of these stocks.

Shout Options

Shout options allow the holder to “shout” to lock in a certain payoff level at one point during the life of the option. The final payoff is the maximum of the shout level or the payoff at maturity.

Example:

Scenario: An investor buys a shout call option on a stock with a strike price of $50. If the stock rises to $60, the investor can "shout" to lock in a payoff based on this level. If the stock rises further to $70, the final payoff is based on $70; if it falls to $55, the payoff is based on $60 (the shout level).

Question 18

Interst rate caps.

Answer 18

Interest-rate caps are essentially a series of call options that expire on specific dates in the future. Caps are purchased to hedge an exposure to rising interest rates.

Cap buyers are able to “cap” or limit the interest expense due on a floating-rate liability.
Cap sellers, or writers, agree to pay cap buyers the amount by which an interest rate (known as the reference rate), exceeds an exercise rate (known as the cap rate), on specific dates in the future, in return for an upfront payment (the premium).

Interest-rate cap agreements specify:

the notional amount – the dollar value used to determine the size of any cap payments;
the reference rate – the interest rate used to determine if a cap payment is triggered (e.g., the Secured Overnight Rate [SOFR]);
the exercise rate (more commonly known as the cap rate) – the rate that the reference rate is compared to, to determine if a cap payment is triggered;
the term – the period covered by the option;
the settlement frequency – the frequency with which the reference rate is compared to the cap rate to determine whether a cap payment is made;
the premium – the amount paid by the buyer to the seller at the onset of the contract.

Question 19

Interest rate floors.

Answer 19

Interest-rate floors are essentially a series of put options that expire on specific dates in the future. Floors are purchased to hedge an exposure to falling interest rates.

Floor buyers are able to put a “floor” under the interest revenue due from a floating-rate asset.
Floor sellers, or writers, agree to pay floor buyers the amount by which an exercise rate (known as the floor rate), exceeds an interest rate (known as the reference rate), on specific dates in the future, in return for an upfront payment (the premium)

Interest-rate floors specify the same things as interest-rate caps, including:

the notional amount;
the reference rate;
the exercise rate;
the term;
the settlement frequency;
the premium.

Question 20

Interest rate collars.

Answer 20

Interest-rate collars are simply a combination of an interest-rate cap and an interest-rate floor. They can be established with two separate transactions – one for the cap and one for the floor – or through a single transaction.

Collars lock the purchaser into a floating rate of interest that is bounded on both the upside and the downside.

Parties with a floating-rate liability can establish a collar by buying a cap and selling a floor with a floor rate that is lower than the cap rate. Buying the cap puts a limit on the party’s interest expense when the reference rate rises above the cap rate. Selling the floor, however, removes the party’s ability to benefit from an interest rate below the floor rate.

The main advantage of a collar relative to the purchase of a cap is that the collar costs less than the cap. The lower cost is a result of the fact that an interest-rate floor is sold and a premium is received. The premium effectively lowers the cost of the cap.
The downside of a collar is that the party must pay the buyer of the floor if the reference rate falls below the floor rate on one of the interest payment dates. Under the cap-only scenario, there is no obligation to pay if rates decline, thereby allowing cap buyers to fully benefit from lower interest rates.