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
10
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：
( )
rt
rt
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.
6)
×=
×
×
00000
44.4
1080 250
=
×
4. Answer: B
S
F
σ
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
1
The bond's duration = 8e 2 8e 3 8e 4 8e 5 108e
86.80
= 4.256
− −× −× −× −×

+× +× +× +×

*
00
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
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
2
12
2
1
Forward rate = Futures rate - TT
2
1
4.8% 0.011 6 6.25 4.57%
2
s
= − × ×× =
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
R
2
is the two-year zero rate:
2
R 2.0
0.10 1.0
11e 111e 100
− ×
− ×
+ =
so that R
2
= 0.1046. The three-year swap rate implies that a three-year LIBOR bond with a coupon
of 12% sells for par. If R
3
is the three-year zero rate:
3
R 3.0
0.10 1.0 0.1046 2.0
12e 12e 112e 100
− ×
− × − ×
+ + =
so that R
3
= 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
2
) 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)
2
(fixed amount)e N(d ) $45e 0.9732 $42.50
− −
= × =
22. Answer: A
The present value of the strike price is
4
0.12
12
60e 57.65
− ×
=
, the present value of the dividend is
1
0.12
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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