Question 1

Which of the following is true about a futures option and a spot option on the same underlying asset when they have the same strike price? The expiration dates of the two options and the futures are all the same.
A)A European call spot option and an American call futures option are equivalent
B)An American call spot option and a European call futures option are equivalent
C)A European put spot option and European put futures option are equivalent
D)An American put spot option and American put futures option are equivalent

Accepted Answer

The two European options are equivalent.This result is often used to price options on spot.

Question 2

Which of the following is true for a September futures option?
A)The expiration month of option is September
B)The option was first traded in September
C)The delivery month of the underlying futures contract is September
D)September is the first month when the option can be exercised

Accepted Answer

The month of a futures option refers to the month of the underlying futures contract.

Question 3

A futures price is currently 40 cents.It is expected to move up to 44 cents or down to 34 cents in the next six months.The risk-free interest rate is 6%.What is the probability of an up movement in a risk-neutral world?
A)0.4
B)0.5
C)0.72
D)0.6

Accepted Answer

The probability of an up movement is (1-d)/(u-d).In this case u is 1.1 and d is 0.85.The probability of an up movement is therefore 0.15/0.25=0.6.

Question 4

Which of the following is NOT true?
A)Black's model can be used to value an American-style option on futures
B)Black's model can be used to value a European-style option on futures
C)Black's model can be used to value a European-style option on spot
D)Black's model is widely used by practitioners

Accepted Answer

Black's model is used for valuing European options.A is therefore clearly false.

Question 5

Which of the following describes a futures-style option?
A)An option on a futures
B)An option on spot with daily settlement
C)A futures on an option payoff
D)None of the above

Accepted Answer

A futures style option is a futures contract on the option payoff

Question 6

What is the expected growth rate of an index futures price in the risk-neutral world?
A)The excess of the risk-free rate over the dividend yield
B)The risk-free rate
C)The dividend yield on the index
D)Zero

Accepted Answer

All futures prices grow at rate zero on average in a risk-neutral world.

Question 7

Which of the following is true?
A)A futures option is settled daily
B)A futures-style option is settled daily
C)Both a futures option and a futures-style option are settled daily
D)Neither a futures option nor a futures-style option is settled daily

Accepted Answer

A futures style like a futures contract is settled daily.Regular options are not settled daily.

Question 8

One-year European call and put options on an asset are worth $3 and $4 respectively when the strike price is $20 and the one-year risk-free rate is 5%.What is the one-year futures price of the asset if there are no arbitrage opportunities? (Use put-call parity.)
A)$19.55
B)$18.95
C)$20.95
D)$20.45

Accepted Answer

Put call parity is
$c + K ^ { - r T } = p + F _ { o } e ^ { - r T }$
Hence
$F _ { 0 } = K + ( c - p ) e ^ { r T } = 20 + ( 3 - 4 ) e ^ { 0.05\times {1} }= \$ 18.95$

Question 9

Which of the following is acquired (in addition to a cash payoff)when the holder of a put futures exercises?
A)A long position in a futures contract
B)A short position in a futures contract
C)A long position in the underlying asset
D)A short position in the underlying asset

Accepted Answer

The holder of the put acquires a short futures position which can be immediately closed out if desired.

Question 10

Consider a European one-year call futures option and a European one-year put futures options when the futures price equals the strike price.Which of the following is true?
A)The call futures option is worth more than the put futures option
B)The put futures option is worth more than the call futures option
C)The call futures option is sometimes worth more and sometimes worth less than the put futures option
D)The call futures option is worth the same as the put futures option

Accepted Answer

Put call parity is
$c + K e ^ { - r T } = p + F _ { o } e ^ { - r T }$
When $\mathrm { F } _ { 0 } = \mathrm { K }$ it follows that $\mathrm { c } = \mathrm { p }$.

Question 11

A futures price is currently 40 cents.It is expected to move up to 44 cents or down to 34 cents in the next six months.The risk-free interest rate is 6%.
-What is the value of a six month call option with a strike price of 39 cents?
A)5.00 cents
B)2.91 cents
C)3.00 cents
D)4.21 cents

Accepted Answer

The probability of an up movement is (1-d)/(u-d).In this case u is 1.1 and d is 0.85.The probability of an up movement is therefore 0.15/0.25=0.6.The option pays off 5 cents if there is an up movement and zero if there is a down movement.The value of the option is therefore 0.6×5×e^-0.06×0.5= 2.91 cents.

Question 12

When Black's model used to value a European option on the spot price of an asset,which of the following is NOT true?
A)It is necessary to know the futures or forward price for a contract maturing at the same time as the option
B)It is not necessary to estimate income on the underlying asset
C)It is not necessary to know the risk-free rate
D)The underlying asset can be an investment or a consumption asset

Accepted Answer

The futures price embodies all the relevant information needed about the spot price and the income on the asset.However,it is still necessary to know the risk-free rate.

Question 13

Which of the following are true?
A)Futures options are usually European
B)Futures options are usually American
C)Both American and European futures options trade actively are exchanges
D)Both American and European futures options trade actively in the OTC market

Accepted Answer

Futures options trade on exchanges and are American.

Question 14

What is the cash settlement if a put futures option on 50 units of the underlying asset is exercised?
A)(Current Futures Price - Strike Price) times 50
B)(Strike Price - Current Futures Price) times 50
C)(Most Recent Futures Settlement Price - Strike Price) times 50
D)(Strike Price - Most Recent Futures Settlement Price) times 50

Accepted Answer

The cash payoff is the strike price minus the most recent futures settlement price times the size of the contract.The party exercising also gets a short futures position which brings the value of what is received at the time of exercise equal to strike price minus the current futures price times the size of the contract.

Question 15

Which of the following is true when the futures price exceeds the spot price?
A)Calls on futures should never be exercised early
B)Put on futures should never be exercised early
C)A call on futures is always worth at least as much as the corresponding call on spot
D)A call on spot is always worth at least as much as the corresponding call on futures

Accepted Answer

If the futures price is above the spot price a call on futures must be worth more than a call on spot.Both calls and puts on futures are sometimes exercised early.

Question 16

A futures price is currently 40 cents.It is expected to move up to 44 cents or down to 34 cents in the next six months.The risk-free interest rate is 6%.
-What is the value of a six-month put option with a strike price of 37 cents?
A)3.00 cents
B)2.91 cents
C)1.16 cents
D)1.20 cents

Accepted Answer

The probability of an up movement is (1-d)/(u-d).In this case u is 1.1 and d is 0.85.The probability of an up movement is therefore 0.15/0.25=0.6.The option pays off zero if there is an up movement and 3 cents if there is a down movement.The value of the option is therefore 0.4×3×e^-0.06×0.5= 1.16 cents.

Question 17

The risk-free rate is 5% and the dividend yield on the S&P 500 index is 2%.Which of the following is correct when a futures option on the index is being valued?
A)The futures price of the S&P 500 is treated like a stock paying a dividend yield of 5%.
B)The futures price of the S&P 500 is treated like a stock paying a dividend yield of 2%.
C)The futures price of the S&P 500 is treated like a stock paying a dividend yield of 3%.
D)The futures price of the S&P 500 is treated like a non-dividend-paying stock.

Accepted Answer

When a futures option is being valued the dividend yield is set equal to the domestic risk-free rate.In this case the domestic risk-free rate is 5%.A is therefore correct.

Question 18

What is the value of a European call futures option where the futures price is 50,the strike price is 50,the risk-free rate is 5%,the volatility is 20% and the time to maturity is three months?
A)49.38N(0.05)-49.38N(-0.05)
B)50N(0.05)-50N(-0.05)
C)49.38N(0.1)-49.38N(-0.1)
D)50N(0.1)-49.38N(-0.1)

Accepted Answer

The formula is
 $\begin{array} { l } 
c = F _ { 0 } e ^ { - r T } N \left( d _ { 1 } \right) - K e ^ { - r T } N \left( d _ { 2 } \right) \
d _ { 1 } = \frac { \ln \left( F _ { 0 } / K \right) + \sigma ^ { 2 } T / 2 } { \sigma \sqrt { T } } \quad d _ { 2 } = d _ { 1 } - \sigma \sqrt { T }
\end{array}$ 
In this case
 $K e ^ { - r T } = F _ { 0 } e ^ { - r T } = 50 e ^ { - 0.05 \times 0.25 } = 48.38$ 
 $d _ { 1 } = \frac { \ln ( 1 ) + 0.2 ^ { 2 } \times 0.25 / 2 } { 0.2 \sqrt { 0.25 } } = 0.05 \quad d _ { 2 } = d _ { 1 } - \sigma \sqrt { T } = - 0.05$ The correct answer is therefore A.

Question 19

What is the cash component of the payoff if a call futures option on 50 units of the underlying asset is exercised?
A)(Current Futures Price - Strike Price) times 50
B)(Strike Price - Current Futures Price) times 50
C)(Most Recent Futures Settlement Price - Strike Price) times 50
D)(Strike Price - Most Recent Futures Settlement Price) times 50

Accepted Answer

When the option is exercised the holder obtains the cash payoff in C and a long futures contract.

Question 20

Which of the following is acquired (in addition to a cash payoff)when the holder of a call futures exercises?
A)A long position in a futures contract
B)A short position in a futures contract
C)A long position in the underlying asset
D)A short position in the underlying asset

Accepted Answer

The holder of the call acquires a long futures position which can be immediately closed out if desired.

Quiz 18: Futures Options

Which of the following is true about a futures option and a spot option on the same underlying asset when they have the same strike price? The expiration dates of the two options and the futures are all the same.

Which of the following is true for a September futures option?

A futures price is currently 40 cents.It is expected to move up to 44 cents or down to 34 cents in the next six months.The risk-free interest rate is 6%.What is the probability of an up movement in a risk-neutral world?

Which of the following is NOT true?

Which of the following describes a futures-style option?

What is the expected growth rate of an index futures price in the risk-neutral world?

Which of the following is true?

One-year European call and put options on an asset are worth $3 and $4 respectively when the strike price is $20 and the one-year risk-free rate is 5%.What is the one-year futures price of the asset if there are no arbitrage opportunities? (Use put-call parity.)

Which of the following is acquired (in addition to a cash payoff) when the holder of a put futures exercises?

Consider a European one-year call futures option and a European one-year put futures options when the futures price equals the strike price.Which of the following is true?

A futures price is currently 40 cents.It is expected to move up to 44 cents or down to 34 cents in the next six months.The risk-free interest rate is 6%. -What is the value of a six month call option with a strike price of 39 cents?

When Black's model used to value a European option on the spot price of an asset,which of the following is NOT true?

Which of the following are true?

What is the cash settlement if a put futures option on 50 units of the underlying asset is exercised?

Which of the following is true when the futures price exceeds the spot price?

A futures price is currently 40 cents.It is expected to move up to 44 cents or down to 34 cents in the next six months.The risk-free interest rate is 6%. -What is the value of a six-month put option with a strike price of 37 cents?

The risk-free rate is 5% and the dividend yield on the S&P 500 index is 2%.Which of the following is correct when a futures option on the index is being valued?

What is the value of a European call futures option where the futures price is 50,the strike price is 50,the risk-free rate is 5%,the volatility is 20% and the time to maturity is three months?

What is the cash component of the payoff if a call futures option on 50 units of the underlying asset is exercised?

Which of the following is acquired (in addition to a cash payoff) when the holder of a call futures exercises?