Chapter 18. Futures options and Black’s model

Question 1

What is a futures option?

Answer 1

A futures option is the right, but not the obligation, to enter into a futures contract at a certain futures price by a certain date.

Question 2

What is a futures call option?

Answer 2

A futures call option is the right to enter into a long futures contract at a certain price.

Question 3

What is a futures put option?

Answer 3

A futures put option is the right to enter into a short futures contract at a certain price.

Question 4

Are futures options generally American or European?

Answer 4

Futures options are generally American; that is, they can be exercised any time during the life of the contract.

Question 5

: What is the effective payoff from a futures call option and a futures put option?

Answer 5

The effective payoff from a futures call option is max(1F - K, 0), and the effective payoff from a futures put option is max(K - F, 0), where F is the futures price at the time of exercise and K is the strike price.

Question 6

What are futures options referred to by?

Answer 6

Futures options are referred to by the delivery month of the underlying futures contract, not by the expiration month of the option.

Question 7

What is the expiration date of a futures option contract?

Answer 7

The expiration date of a futures option contract is usually a short period of time before the last trading day of the underlying futures contract.

Question 8

What are options on interest rate futures?

Answer 8

Options on interest rate futures are contracts traded by the CME Group that give the holder the right, but not the obligation, to enter into a futures contract for a specific interest rate at a certain price.

Question 9

How are interest rate futures prices affected by changes in bond prices?

Answer 9

Interest rate futures prices increase when bond prices increase (i.e., when interest rates fall) and decrease when bond prices decrease (i.e., when interest rates rise).

Question 10

How do interest rate futures options work?

Answer 10

Interest rate futures options work in the same way as other futures options contracts. The holder of a call option obtains a long position in the futures contract when the option is exercised, and the option writer obtains a corresponding short position. The total payoff from the call, including the value of the futures position, is max1(F - K, 0) where F is the futures price at the time of exercise and K is the strike price.

Question 11

How can an investor speculate on rising or falling interest rates with interest rate futures options?

Answer 11

An investor who thinks that short-term interest rates will rise can speculate by buying put options on Eurodollar or SOFR futures, whereas an investor who thinks the rates will fall can speculate by buying call options on Eurodollar or SOFR futures. An investor who thinks that long-term interest rates will rise can speculate by buying put options on Treasury note futures or Treasury bond futures, whereas an investor who thinks the rates will fall can speculate by buying call options on these instruments.

Question 12

What is the main reason why people choose to trade options on futures rather than options on the underlying asset?

Answer 12

The main reason appears to be that a futures contract is more liquid and easier to trade than the underlying asset, and the futures price is known immediately from trading on the futures exchange.

Question 13

What is an advantage of settling futures options in cash?

Answer 13

Settling futures options in cash is appealing to many investors, particularly those with limited capital who may find it difficult to come up with the funds to buy the underlying asset when an option on spot is exercised.

Question 14

Futures-style options are a bet on what the payoff from an option will be, just as a futures contract is a bet on what the future price of an asset will be.

Answer 14

If interest rates are constant, the futures price in a futures-style option is the same as the forward price in a forward contract on the option payoff, which is the current option price compounded forward at the risk-free rate as analyzed in Chapter 5.

Question 15

Traders who buy or sell futures-style options post margin in the same way as a regular futures contract, settling the contract daily with the final settlement price being the payoff from the option.

Answer 15

Futures-style options are a way to bet on the payoff from an option and have the same futures price as the forward price in a forward contract on the option payoff when interest rates are constant.

Question 16

What are futures-style options?

Answer 16

Futures-style options are futures contracts on the payoff from an option. Traders who buy or sell a futures-style option post margin in the same way that they do on a regular futures contract. The contract is settled daily as with any other futures contract and the final settlement price is the payoff from the option.

Question 17

Why are American futures options worth more than European futures options?

Answer 17

Assuming that the risk-free rate of interest, r, is positive, there is always some chance that it will be optimal to exercise an American futures option early. American futures options are therefore worth more than their European counterparts.

Question 18

When are American futures options worth more/less than their corresponding American spot options?

Answer 18

In a normal market with futures prices consistently higher than spot prices prior to maturity, an American futures call option must be worth more than the corresponding American spot call option. Similarly, an American futures put option must be worth less than the corresponding American spot put option. In an inverted market with futures prices consistently lower than spot prices, the reverse must be true.

Question 19

Futures-style options are traded on some European exchanges and are futures contracts on the payoff from an option.

Answer 19

Traders who buy or sell a futures-style option post margin instead of paying/receiving cash up front. The contract is settled daily and the final settlement price is the payoff from the option.

Question 20

What happens when a futures option is exercised?

Answer 20

When a call is exercised, the holder acquires a long futures position plus a cash amount equal to the excess of the futures price over the strike price. When a put is exercised, the holder acquires a short position plus a cash amount equal to the excess of the strike price over the futures price. The futures contract that is delivered usually expires slightly later than the option.

Question 21

How does the pricing of European futures options compare to that of European spot options?

Answer 21

If the expiration dates for the option and futures contracts are the same, a European futures option is worth exactly the same as the corresponding European spot option. This result is often used to value European spot options. The result is not true for American options.

Question 22

How does the behavior of a futures price compare to that of a stock that provides a dividend yield equal to the risk-free rate?

Answer 22

A futures price behaves in the same way as a stock that provides a dividend yield equal to the risk-free rate, r. This means that the results produced in Chapter 17 for options on a stock paying a dividend yield apply to futures options if we replace the stock price by the futures price and set the dividend yield equal to the risk-free interest rate. Pricing formulas for European futures options were first produced by Fischer Black in 1976. They assume that the futures price is lognormally distributed at the option’s expiration.