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FRM一级模拟考试（二）答案1

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2020 年 10 月 FRM 一级模拟考试（二）_参考答案The sum of the price of an up-and-in barrier call

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2020

年

月

FRM

一级模拟考试（二）

参考答案

1. Answer: B

The sum of the price of an up-and-in barrier call and an up-and-out barrier call is the price of an

otherwise equivalent European call. The price of the European call is EUR 3.52 + EUR 1.24 =

EUR 4.76.

The sum of the price of a down-and-in barrier put and a down-and-out barrier put is the price of an

otherwise equivalent European put. The price of the European put is EUR 2.00 + EUR 1.01 =

EUR 3.01.

Using put-call parity, where C represents the price of a call option and P the price of a put option：

( )

0.02 1

C Ke P S

K e (P S C)

Hence,K e 3.01 40.96 4.76 40.00

−

+=+

= +−

= +−=

2. Answer: D

The margin required the second day = 20 × 2000 = 40,000.

The first day’s contracts have a gain of (50,200 – 50,000) × 100 = 20,000.

The second day’s contracts have a loss of (51,000 – 50,200) × 20 = 16,000.

So the member should add the margin 40,000 + 16,000 – 20,000 = 36,000.

3. Answer: A

20000000

In order to minimize the risk, the company should sell the contract = 1.2 88.9

1080 250

In order the coto mpareduce ny sho the beta of uld sell the the portfolio to 0.6, contract

200

= (1.2-0.

×=

00000

44.4

1080 250

4. Answer: B

0.65

The optimal hedge ratio

ρ 0.8 0.642 64.2%

σ 0.81

==×= =

5. Answer: A

DV01 may not be a reliable measure when changes in interest rates are not small. Also,

when applying DV01 we assume that the yield curve shifts are parallel.

6. Answer: A

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When the term structure of interest rates is upward-sloping, the forward rate > the zero rate >

the yield.

When the term structure of interest rates is downward-sloping, the yield > the zero rate > the

forward rate.

7. Answer: D

Long two 10-year 4% coupon bond, short one 10-year 8% coupon bond, then the coupon will

offset. The present cash flow is 90 – 2 × 80 = -70, the cash flow after 10 year is 200 – 100 = 100.

Considering continuously compounding, so the spot rate is

10r

70 e 100, r 3.57%×= =

8. Answer: C

The call option is deep in-the-money and must have a delta close to one. The put option

is deep out-of-the-money and must have a delta close to zero. Therefore, when the

underlying stock falls by USD 1, the value of the deep in-the-money call will decrease by

close to USD 1, and the value of the deep out-of-the-money put will increase by an amount

very close to zero. The choice that is closest to satisfying both conditions is C.

9. Answer: A

0.11 0.11 2 0.11 3 0.11 4 0.11 5

The bond's price = 8e 8e 8e 8e 108e 86.80

− −× −× −× −×

++++ =

0.11 0.11 2 0.11 3 0.11 4 0.11 5

The bond's duration = 8e 2 8e 3 8e 4 8e 5 108e

86.80

= 4.256

− −× −× −× −×



+× +× +× +×



4.256

P =P MD *P * y=86.80 * 86.80 * -0.2% =87.4656

1 11%

− D−

（）

10. Answer: A

As yields in the market declines, the probability that the call option will get exercised

increases. This causes the price to reduce relative to an otherwise comparable option free

bond, which is also known as a negative convexity.

11. Answer: C

The average dividend = (3 × 2% + 2 × 5%)/5 = 3.2%

So the futures’ price =

(9% 3.2%) 5/12

300e 307.34

−×

12. Answer: A

(0.08 0.03) 2/12

0.65e 0.6554 0.66

−×

= <

So the arbitrage opportunity is to borrow US dollars to buy Swiss franc and sell Swiss franc

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futures.

13. Answer: C

When an asset is strongly negatively correlated with interest rates, futures prices will tend to

be slightly lower than forward prices. When the underlying asset increases in price, the

immediate gain arising from the daily futures settlement will tend to be invested at a lower

than average rate of interest due to the negative correlation. In this case futures would sell

for slightly less than forward contracts, which are not affected by interest rate movements in

the same manner since forward contracts do not have a daily settlement feature.

The other three choices would all most likely result in the futures price being higher than the

forward price.

14. Answer: B

Forward rate = Futures rate - TT

4.8% 0.011 6 6.25 4.57%

= − × ×× =

15. Answer: D

The treasurer should short Treasury bond futures contract. If bond prices go down, this futures

position will provide offsetting gains. The number of contracts that should be shorted is:

10,000,000 × 7.1/(91,375 × 8.8) = 88.30

88 contracts should be shorted.

16. Answer: A

When rates drop, the long position in the futures and the short position in the FRA both gain.

17. Answer: C

( )

0.1 4/12 0.1 10/12

0.1 4/12

Fix :6e 106e 103.328

Floating : 100 4.8 e 101.364

103.328 101.364 1.964

−× −×

−×

−=

18. Answer: C

Pay dollars:

( )

1/4 5/4

30 1 10%

30 10%

32.9161

1 8% 1 8%

×+

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Receive sterling:

( )

1/4 5/4

20 1 14% 1.65

20 14% 1.65

37.5201

1 11% 1 11%

× + ×

× ×

+ =

+ +

37.5201 – 32.9161 = 4.604

19. Answer: A

A corporation can issue floating-rate notes and use an interest rate swap agreement to convert it to

fixed-rate debt.

20. Answer: A

The two-year swap rate implies that a two-year LIBOR bond with a coupon of 11% sells for par. If

is the two-year zero rate:

R 2.0

0.10 1.0

11e 111e 100

− ×

+ =

so that R

= 0.1046. The three-year swap rate implies that a three-year LIBOR bond with a coupon

of 12% sells for par. If R

is the three-year zero rate:

R 3.0

0.10 1.0 0.1046 2.0

12e 12e 112e 100

− ×

− × − ×

+ + =

so that R

= 0.1146. The two- and three-year rates are therefore 10.46% and 11.46% with

continuous compounding.

21. Answer: B

Since the Black-Scholes-Merton formula denotes N(d

) as the probability of the asset price being

above the strike price, the value of a cash-or-nothing call is equal to:

rT 0.03(1)

(fixed amount)e N(d ) $45e 0.9732 $42.50

− −

= × =

22. Answer: A

The present value of the strike price is

0.12

60e 57.65

− ×

, the present value of the dividend is

0.12

0.80e 0.79

− ×

. 5 < 64 - 57.65 - 0.79 = 5.56, so the option is undervalued.

If the stock’s price falls below USD 60, the arbitrageur will have a loss of USD 5.

If the stock’s price are higher than USD 60, the arbitrageur will get a gain of 64 - 57.65 - 0.79 – 5

= 0.56.

23. Answer: C

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