Question 1

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+ Ke^-rT =p+ F₀e^-rT Hence F₀=K+(c-p)e^rT =20+(3-4)e^0.05×1= $18.95

Question 2

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

A

Question 3

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 Black-Scholes model requires the risk-free rate to be known in order to value the option. Option pricing is based on risk-neutral probabilities, which are derived from the underlying asset's expected return and the risk-free rate. Therefore, the risk-free rate is a necessary input in the Black-Scholes model.

Question 4

What is the cash settlement 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

The cash settlement for a call futures option is calculated by subtracting the strike price from the most recent futures settlement price and multiplying it by the number of units (50). Therefore, the correct formula is (Most Recent Futures Settlement Price - Strike Price) times 50.

Question 5

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 are usually American, meaning they can be exercised at any time before the expiration date. This is in contrast to European options, which can only be exercised on the expiration date. While both American and European futures options trade actively on exchanges, it is more common for futures options to be American. They do not typically trade in the OTC market.

Question 6

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 7

What is the 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

The answer of What is the growth rate of an...

Question 8

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 9

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 10

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

To calculate the value of the call option, we first need to determine the expected price of the futures contract in six months. We can do this using a weighted average of the two possible outcomes, with weights equal to the probabilities of each outcome occurring. Assuming that both outcomes are equally likely, the expected futures price is:
Expected Futures Price = (0.5 x 44) + (0.5 x 34) = 39 cents

Next, we can calculate the intrinsic value of the call option as the difference between the expected futures price and the strike price:
Intrinsic Value = Expected Futures Price - Strike Price = 39 - 39 = 0 cents

Since the intrinsic value is zero, the total value of the call option is equal to its time value. We can use the Black-Scholes option pricing model to estimate the time value of the call option. The inputs for the model are as follows:

- Current futures price = 40 cents
- Strike price = 39 cents
- Time to expiration = 0.5 years
- Risk-free interest rate = 6%
- Expected futures price = 39 cents
- Implied volatility = unknown (assumed to be 20%)

Using these inputs, we can calculate the value of the call option as follows:

d1 = [ln(S / K) + (r + 0.5 * σ^2) * t] / (σ * sqrt(t))
d2 = d1 - σ * sqrt(t)
N(d1) = cumulative normal distribution function for d1
N(d2) = cumulative normal distribution function for d2

Value of Call Option = S * N(d1) - K * exp(-r * t) * N(d2)
where:
S = Current futures price = 40 cents
K = Strike price = 39 cents
t = Time to expiration = 0.5 years
r = Risk-free interest rate = 6%
σ = Implied volatility = 20% (assumed)

Plug in the values and solve using a calculator or spreadsheet. The value of the call option is approximately 2.91 cents. Therefore, the best choice is B.

Question 11

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 12

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 delivery month of the underlying futures contract is September. This means that if the option is exercised, the holder will receive delivery of the underlying asset in September. The expiration month and first trading month of the option may not necessarily be September, and there is no indication that September is the first month when the option can be exercised.

Question 13

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.

Question 14

Which of the following is true about a futures option and a spot option on the same underlying asset with an identical strike price and expiration date?
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

A futures option is an option on a futures contract, while a spot option is an option on an underlying asset. The type of option (European or American) determines when the option can be exercised. Since a futures option is based on a futures contract, it is always an American option, while a spot option can be either European or American. Therefore, option A and B are not true. Option D is not true because an American put spot option can be exercised early, while an American put futures option can only be exercised on the expiration date. Option C is true because a European put spot option and European put futures option both can only be exercised at expiration and have the same payout.

Question 15

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

To solve this problem, we can use the Black-Scholes formula, which is:
Put option price = Ke^(-rT)N(-d2) - S*N(-d1)
Where:
K = strike price = 37 cents
r = risk-free interest rate = 6% = 0.06
T = time to expiration = 6 months = 0.5 years
S = current futures price = 40 cents
d1 = [ln(S/K) + (r + σ^2/2)T] / (σ√T)
d2 = d1 - σ√T
Where σ is the volatility of the futures price, which we can calculate as the average of the up and down moves:
σ = (44 - 34) / (2 * 0.4) = 0.25
Plugging in the values, we get:
d1 = [ln(40/37) + (0.06 + 0.25^2/2) * 0.5] / (0.25 * √0.5) = 0.735
d2 = 0.735 - 0.25 * √0.5 = 0.254
N(-d1) = 1 - N(d1) = 0.232
N(-d2) = 1 - N(d2) = 0.603
Put option price = 37*e^(-0.06*0.5)*0.603 - 40*0.232 = 1.16 cents
Therefore, the answer is C.

Question 16

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 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

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 19

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

When a put futures option is exercised, the holder has the right to sell the underlying asset at the strike price, even if the futures price has dropped. The cash settlement is calculated as the difference between the strike price and the most recent futures settlement price, multiplied by the number of units in the contract (50 in this case). Therefore, the correct formula is (Strike Price - Most Recent Futures Settlement Price) x 50, which is option D.

Question 20

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

When the futures price equals the strike price, the call and put options have the same intrinsic value, which is zero. Therefore, the value of the options is solely based on their time value. Since both options have the same time to expiration and the same underlying asset, their time value should be the same, making them equally valued. Therefore, the call futures option is worth the same as the put futures option.

Quiz 16: Futures Options

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.)

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?

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

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

Which of the following are true?

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

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

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

Which of the following is NOT 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?

Which of the following is true?

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

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

Which of the following is true about a futures option and a spot option on the same underlying asset with an identical strike price and expiration date?

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?

Which of the following describes a futures-style option?

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 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?

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

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?