Question 1

Consider an option to buy £10,000 for €12,500.In the next period,if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent.On the other hand,the euro could depreciate against the pound by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.
 
$
\begin{array}{lll}
&spot Rates&Risk-tree Rates\
S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \
S_{0}\left(\$ /  £)\right. & \$ 2.00=£ 1.00&i €4.00 \%  \
S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%
\end{array}
$ Calculate the hedge ratio.

Accepted Answer

The answer of Consider an option to buy £10,000 for...

Question 2

The Black-Scholes option pricing formula
A)is used widely in practice,especially by international banks in trading OTC options.
B)is not widely used outside of the academic world.
C)works well enough,but is not used in the real world because no one has the time to flog their calculator for five minutes on the trading floor.
D)none of the options

Accepted Answer

The Black-Scholes option pricing formula is widely used in practice, especially by international banks in trading OTC options.

Question 3

Find the Black-Scholes price of a six-month call option written on €100,000 with a strike price of $1.00 = €1.00.The current exchange rate is $1.25 = €1.00; The U.S.risk-free rate is 5 percent over the period and the euro-zone risk-free rate is 4 percent.The volatility of the underlying asset is 10.7 percent. A)C_e = $0.63577 B)C_e = $0.0998 C)C_e = $1.6331 D)none of the options

Accepted Answer

The Black-Scholes formula for a call option on foreign currency is used here. Given the inputs, the calculated call option price is approximately $0.63577.

Question 4

Find the input d₁ of the Black-Scholes price of a six-month call option written on €100,000 with a strike price of $1.00 = €1.00.The current exchange rate is $1.25 = €1.00; The U.S.risk-free rate is 5% over the period and the euro-zone risk-free rate is 4%.The volatility of the underlying asset is 10.7 percent. A)d₁ = 0.103915 B)d₁ = 2.9871 C)d₁ = 0.0283 D)none of the options

Accepted Answer

The input d₁ is calculated using the Black-Scholes formula: d₁ = [ln(S/K) + (r - rf + 0.5*σ²)T] / (σ√T). Substituting the given values: S = 1.25, K = 1.00, r = 0.05, rf = 0.04, σ = 0.107, T = 0.5, we get d₁ = 0.103915.

Question 5

Consider an option to buy £10,000 for €12,500.In the next period,if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent.On the other hand,the euro could depreciate against the pound by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.
 
$
\begin{array}{lll}
&spot Rates&Risk-tree Rates\
S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \
S_{0}\left(\$ /  £)\right. & \$ 2.00=£ 1.00&i €4.00 \%  \
S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%
\end{array}
$ USING RISK NEUTRAL VALUATION (i.e.,the binomial option pricing model)find the value of the call (in euro).

Accepted Answer

The answer of Consider an option to buy £10,000 for...

Question 6

With regard to trading costs,
A)forward contracts involve the bid-ask spread plus the broker's commission.
B)futures contracts involve the bid-ask spread plus the broker's commission.
C)futures contracts involve the bid-ask spread plus indirect bank charges via compensating balance requirements.
D)none of the options

Accepted Answer

Futures contracts involve trading costs such as bid-ask spread (the difference between the highest price a buyer is willing to pay and the lowest price a seller is willing to accept) and the broker's commission. Forward contracts, on the other hand, involve bid-ask spread plus other costs such as credit risk, counterparty risk, and funding costs. Indirect bank charges via compensating balance requirements are not directly related to trading costs.

Question 7

Consider an option to buy £10,000 for €12,500.In the next period,if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent.On the other hand,the euro could depreciate against the pound by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.
 
$
\begin{array}{lll}
&spot Rates&Risk-tree Rates\
S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \
S_{0}\left(\$ /  £)\right. & \$ 2.00=£ 1.00&i €4.00 \%  \
S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%
\end{array}
$ State the composition of the replicating portfolio; your answer should contain "trading orders" of what to buy and what to sell at time zero.

Accepted Answer

The answer of Consider an option to buy £10,000 for...

Question 8

Empirical tests of the Black-Scholes option pricing formula
A)have faced difficulties due to nonsynchronous data.
B)suggest that when using simultaneous price data and incorporating transaction costs they conclude that the PHLX American currency options are efficiently priced.
C)suggest that the European option-pricing model works well for pricing American currency options that are at- or out-of-the money,but does not do well in pricing in-the-money calls and puts.
D)all of the options

Accepted Answer

The statement mentions difficulties faced in empirical tests due to nonsynchronous data, but also suggests that when using simultaneous price data and incorporating transaction costs, the PHLX American currency options are efficiently priced. Additionally, it mentions that the European option-pricing model works well for pricing American currency options that are at- or out-of-the money, but not for pricing in-the-money calls and puts. Therefore, all of the options (A, B, and C) are correct.

Question 9

Find the dollar value today of a 1-period at-the-money call option on €10,000.The spot exchange rate is €1.00 = $1.25.In the next period,the euro can increase in dollar value to $2.00 or fall to $1.00.The interest rate in dollars is i_$ = 27.50%; the interest rate in euro is $i _ {€ } = 2 \%$ . A)$3,308.82 B)$0 C)$3,294.12 D)$4,218.75

Accepted Answer

The call option's payoff is calculated based on the potential future exchange rates and the current interest rates. The expected payoff is discounted back to present value using the dollar interest rate.

Question 10

Suppose that you have written a call option on €10,000 with a strike price in dollars.Suppose further that the hedge ratio is ¹/₂.Which of the following would be an appropriate hedge for a short position in this call option? A)Buy €5,000 today at today's spot exchange rate. B)Agree to buy €5,000 at the maturity of the option at the forward exchange rate for the maturity of the option that prevails today . C)Buy the present value of €5,000 discounted at i€ for the maturity of the option. D)Agree to buy €5,000 at the maturity of the option at the forward exchange rate for the maturity of the option that prevails today or buy the present value of €5,000 discounted at i€ for the maturity of the option.

Accepted Answer

The appropriate hedge for a short position in this call option would be to buy €5,000 at the maturity of the option at the forward exchange rate for the maturity of the option that prevails today, or buy the present value of €5,000 discounted at i€ for the maturity of the option. This is because the hedge ratio suggests that the hedge should involve both euro and dollars, and the options contract involves a fixed euro amount. Option D allows for the purchase of euros at a fixed exchange rate in the future, which mitigates the risk of exchange rate fluctuations affecting the value of the option. Additionally, the present value of €5,000 discounted at i€ for the maturity of the option can also serve as a hedge as it involves the purchase of euros at a fixed rate, even though it is done in the present.

Question 11

Empirical tests of the Black-Scholes option pricing formula
A)shows that binomial option pricing is used widely in practice,especially by international banks in trading OTC options.
B)works well for pricing American currency options that are at-the-money or out-of-the-money.
C)does not do well in pricing in-the-money calls and puts.
D)works well for pricing American currency options that are at-the-money or out-of-the-money,but does not do well in pricing in-the-money calls and puts.

Accepted Answer

Empirical tests have shown that the Black-Scholes option pricing formula works well for pricing American currency options that are at-the-money or out-of-the-money. However, it does not do well in pricing in-the-money calls and puts. In practice, binomial option pricing is also widely used, especially by international banks in trading OTC options.

Question 12

Which of the following is correct?
A)The value (in dollars)of a call option on £5,000 with a strike price of $10,000 is equal to the value (in dollars)of a put option on $10,000 with a strike price of £5,000 only when the spot exchange rate is $2 = £1.
B)The value (in dollars)of a call option on £5,000 with a strike price of $10,000 is equal to the value (in dollars)of a put option on $10,000 with a strike price of £5,000.

Accepted Answer

The answer of Which of the following is correct?
A)The value...

Question 13

With regard to contractual size,
A)forward contracts are characterized by a standardized amount of the underlying asset.
B)futures contracts are tailor-made to the needs of the participant.
C)futures contracts are characterized by a standardized amount of the underlying asset.
D)none of the options

Accepted Answer

Futures contracts are characterized by a standardized amount of the underlying asset. This means that every futures contract of a particular commodity or financial instrument will have the same size or quantity of units. This standardization allows for easier trading and liquidity in the market. In contrast, forward contracts are typically tailored to the specific needs of the participants and may vary in size and terms.

Question 14

The one-step binomial model assumes that at the end of the option period,the call will have appreciated to S_uT = S₀u or depreciated to S_dT = S₀d.How is u calculated? A)1/d B)e^(σt^0.5) C)both 1/d and e^(σt^0.5) D)none of these options

Accepted Answer

In the one-step binomial model, the up factor $u$ can be calculated in different ways depending on the specific assumptions of the model. One common approach is to set $u = \frac{1}{d}$, where $d$ is the down factor, implying that the up movement is the inverse of the down movement. Another approach uses the formula $u = e^{\sigma\sqrt{t}}$, where $\sigma$ is the volatility of the underlying asset and $t$ is the time to expiration. Both methods are used in practice, making option C correct.

Question 15

Consider an option to buy £10,000 for €12,500.In the next period,if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent.On the other hand,the euro could depreciate against the pound by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.
 
$
\begin{array}{lll}
&spot Rates&Risk-tree Rates\
S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \
S_{0}\left(\$ /  £)\right. & \$ 2.00=£ 1.00&i €4.00 \%  \
S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%
\end{array}
$ Calculate the current €/£ spot exchange rate.

Accepted Answer

The answer of Consider an option to buy £10,000 for...

Question 16

Use the European option pricing formula to find the value of a six-month call option on Japanese yen.The strike price is $1 = ¥100.The volatility is 25 percent per annum; r_$ = 5.5% and r_¥ = 6%. A)0.005395 B)0.005982 C)$0.006137/¥ D)none of the options

Accepted Answer

Using the European option pricing formula, we have:

d1 = [ln(S0/K) + (rS1U1B1¥S1U1B0 + σ²/2)T] / (σ√T)
d1 = [ln(1/100) + (0.06 + 0.25²/2)(0.5)] / (0.25√0.5) = -2.5507
d2 = d1 - σ√T = -2.5507 - 0.25√0.5 = -3.0901
N(d1) = 0.005644
N(d2) = 0.002090
C = SN(d1) - Ke^(-rS1U1B1T)N(d2) = 1*0.005644 - 100*0.002090*e^(-0.06*0.5) = $0.006137/¥

Question 17

With regard to trading location,
A)forward contracts are traded competitively on organized exchanges.
B)futures contracts are traded competitively on organized exchanges.
C)futures contracts are traded by bank dealers via a network of telephones and computerized dealing systems.
D)none of the options

Accepted Answer

Futures contracts are traded competitively on organized exchanges, such as the Chicago Mercantile Exchange or the New York Mercantile Exchange. This means that buyers and sellers come together in a centralized location to trade standardized contracts in a transparent, regulated environment. This ensures that all participants have access to the same information and prices, and reduces the risk of fraud or manipulation.

Question 18

Consider an option to buy £10,000 for €12,500.In the next period,if the pound appreciates against the dollar by 37.5 percent then the euro will appreciate against the dollar by ten percent.On the other hand,the euro could depreciate against the pound by 20 percent.
Big hint: don't round,keep exchange rates out to at least 4 decimal places.
 
$
\begin{array}{lll}
&spot Rates&Risk-tree Rates\
S_{0}(\$ / €) & \$ 1.60=€ 1.00&i \$ 3.00 \% \
S_{0}\left(\$ /  £)\right. & \$ 2.00=£ 1.00&i €4.00 \%  \
S_{0}\left(€ /£)\right. & € 1.25=£ 1.00&i £4.00 \%
\end{array}
$ Find the risk neutral probability of an "up" move.

Accepted Answer

The answer of Consider an option to buy £10,000 for...

Question 19

Find the input d₁ of the Black-Scholes price of a six-month call option on Japanese yen.The strike price is $1 = ¥100.The volatility is 25 percent per annum; r_$ = 5.5% and r_¥ = 6%. A)d₁ = 0.074246 B)d₁ = 0.005982 C)d₁ = $0.006137/¥ D)none of the options

Accepted Answer

Using the Black-Scholes formula, we have:

d1 = [ln(S/K) + (r+S12U1B2/2)t] / (S12U1B2t)
= [ln(1/100) + (0.055+0.25/2)0.5] / (0.25*0.5)
= -1.440604

d2 = d1 - S12U1B2t 
= -1.440604 - 0.25*0.5
= -1.565302

N(d1) = 0.074246 (from normal distribution table)

N(d2) = 0.065972 (from normal distribution table)

Therefore, the Black-Scholes price of the call option is:

C = SN(d1) - Ke-rS1U1B1tN(d2)
= 1*N(0.074246) - 100*exp(-0.06*0.5)*N(0.065972)
= $0.005982 or ¥0.5982

So the input dS1U1B11S1U1B0 is 0.074246.

Question 20

With regard to expiration date,
A)futures contracts do not have delivery dates.
B)forward contracts have standardized delivery dates.
C)futures contracts have tailor-made delivery dates that meet the needs of the investor.
D)futures contracts have standardized delivery dates.

Accepted Answer

Futures contracts have standardized delivery dates, which are usually designated by the exchange on which the contract trades. This standardization allows for more liquidity and easier trading of futures contracts. Additionally, it ensures that all parties involved in the contract are aware of the delivery date and can plan accordingly.

Quiz 7: Futures and Options on Foreign Exchange

The Black-Scholes option pricing formula

With regard to trading costs,

Empirical tests of the Black-Scholes option pricing formula

Suppose that you have written a call option on €10,000 with a strike price in dollars.Suppose further that the hedge ratio is 1/2.Which of the following would be an appropriate hedge for a short position in this call option?

Empirical tests of the Black-Scholes option pricing formula

Which of the following is correct?

With regard to contractual size,

The one-step binomial model assumes that at the end of the option period,the call will have appreciated to SuT = S0u or depreciated to SdT = S0d.How is u calculated?

Use the European option pricing formula to find the value of a six-month call option on Japanese yen.The strike price is $1 = ¥100.The volatility is 25 percent per annum; r$ = 5.5% and r¥ = 6%.

With regard to trading location,

Find the input d1 of the Black-Scholes price of a six-month call option on Japanese yen.The strike price is $1 = ¥100.The volatility is 25 percent per annum; r$ = 5.5% and r¥ = 6%.

With regard to expiration date,

Suppose that you have written a call option on €10,000 with a strike price in dollars.Suppose further that the hedge ratio is ¹/₂.Which of the following would be an appropriate hedge for a short position in this call option?

The one-step binomial model assumes that at the end of the option period,the call will have appreciated to S_uT = S₀u or depreciated to S_dT = S₀d.How is u calculated?

Use the European option pricing formula to find the value of a six-month call option on Japanese yen.The strike price is $1 = ¥100.The volatility is 25 percent per annum; r_$ = 5.5% and r_¥ = 6%.

Find the input d₁ of the Black-Scholes price of a six-month call option on Japanese yen.The strike price is $1 = ¥100.The volatility is 25 percent per annum; r_$ = 5.5% and r_¥ = 6%.