THE UNIVERSITY OF HONG KONG

B.ENG. EXAMINATIONS

DEPARTMENT OF INDUSTRIAL AND MANUFACTURING SYSTEMS ENGINEERING

(IMSE 4110) FINANACIAL ENGINEERING

May 18, 2018 Time: 9:30 am - 12:30 pm

Answer 企~ questions. Each of short answer questions carries ~

marks and each of long answer questions carries 旦旦 marks.

Use of Calculators:

“Only approved calculators as announced by the Examinations Secretary can

be used in this examination. It is candidates' responsibility to ensure that
their calculator operates satisfactorily, and candidates must record the name
and 句rpe of the calculator used on the front page of the examination script."

(IMSE4110 - page 1 of 6)
 Short Answer Questions {40 marks)

(1) A deposit account pays 14% per annum with continuous compounding, but interest
is actually paid quarterly. How much interest will be paid each quarter on a $10,000
deposit? (4 marks)

(2) Explain why an FRA is equivalent to the exchange of a floati時 rate of interest for a
fixed rate of interest? (4 marks)

(3 )“An interest rate swap where 6-month LIBOR is exchanged for a fixed rate of 5% on a
principal of $100 million for 6 years involves a known cash flow and a portfolio of eleven
FRAs. ” Why? (4 marks)

(4) What is the difference between the forward price and the value of a forward contract?
(4 marks)

(5) What is (a) an investment asset and (b) a consumption asset? (4 marks)

(6) Why is the distinction between investment and consumption assets important in the
determination of forward and futures prices? (4 marks)

(7) A compa叮 declares a 3-for-1 stock split. Explain how the terms change for a call option
with a strike price of $60. (4 marks)

(8) Give two reasons why the early exercise of an American call option on a non-dividen
paying stock is .not optimal. The first reason should involve the time value of money.
The second reason should apply even if interest rates are zero. (4 marks)

(9) What is meant by writing a covered call? What position in put options is equivalent to
a covered call? (4 mar ks)

(10) Explain the risk-neutral valuation approaches to valuing a European option using a
one-step binomial tree. (4 mar ks)

(IMSE4110 - page 2 of 6)
Long Answer Questions (60 marks)

Question 1 (10 marks)

The HSBC stock price is currently $100. At the end of 3 months it will be either $110 or
$80. The risk-free interest rate (quarterly compound) is 4% per annum. What is the value
of a 3-month European call option with a strike price of $100? Calculate your answer to this
problem using

i) the replication method. (5 marks)

ii) the risk-neutral method. (5 marks)

Question 2 (10 marks)

Alibaba is currently trading at $100.5 per share. You believe that Alibaba will have an
expected return of 8% with volatility of 24.1% per year, while annual interest rates are a七
0.95%. What is the price of an European put on Alibaba with a strike price of $100 and
maturity of 1 ye位？ (Hint: The price of an European call is given by

C(S, K, T) = SN(d1) - KR-T N(d2)

where d1 ＝如何／于1+1σVI'，也＝
σJ于 2 迢
d，1 一 σ而. Use the attached Normal distribution table to
find the values of N(d1) and N(d2). )

Question 3 (10 marks)

An investor currently has $SOM in the Microsoft stock and $50M in one-year zero-coupon
bonds. Assume that the one-year interest rate is 8% (annually compound). Assume that
the current quote on the Microsoft stock is 1,350, each futures contract is written on 200
shares of the Microsof七 stock and the dividend yield on the stock is approximately 3% per
year, i.e., $1,000 invested in the stock yields $30 in dividends at the end of the year.

i) Suppose you invest $1,350 × 200 in one-year zero-coupon bonds and at the same time
enter into a single futures contract with long position on the Microsoft with one year
to maturity. Assume 他的 in one year the stock finishes at 1,200. What is the total
value of your position? How does this compare with buying 200 shares of the stock and
holding them for a year? (5 marks)

ii) If this pension plan decides to switch to a 70/30 stock/bo叫 mix for a period of one
year, how would you implement this strategy using the Microsof七 futures? How many
contracts with one year to maturity would you need? (5 marks)

(IMSE4110 - page 3 of 6)
Question 4 (10 mar ks)

Spot price for copper is $162. 70 per ton and the 12-month copper futures is traded at
$158.00. The 1-year interest rate is 3% (annually compounded).

i) What is the net convenience yield (annually compound) on copper for the 12 month
period? (5 marks)

ii) You need 1,000 tons of copper in 12 months. How would you lock into a price today
using the futures contracts? (The size for each copper futures contract is 100 tons.) (5
marks)

Question 5 (10 marks)

HK government has just made a $10 million issue (face value) of floating rate bonds on
which it pays an interest rate 2% over the HIBOR rate. The bonds are selling at par value.
The HK government is worried that rates are about to rise, and it would like to lock in
a 宜xed interest rate on its borrowings. The HK government sees that dealers in the swap
market are offering swaps of HIBOR for 8%.

i) What interest rate swap will convert the HK governments interest obligation into one
resembling a synthetic fixed-rate loan? (5 marks)

ii) What interest rate will the firm pay on that synthetic fixed-rate loan? (5 m訂ks)

Question 6 (10 marks)

You are a bond trader and see on your screen the following information on three bonds
with annual coupon payments and par value of $100:

Bond Coupon rate(%) Maturity (year) YTM(%)

A O 1 6.00
B 5.5 2 6.50
C 7 3 7.00

Coupon payments are annual.

(i) What are the prices of the above bonds? (5 marks)

(ii) Construct the current term-structure of spot interest rates. (5 marks)

(IMSE4110 - page 4 of 6)
 Appendix

STANDARD NORMAL DISTRIBUTION: Table Values Repr AREA to the LEFT of the Z
z .00 ,01 .02 .03 .04 .05 .06 .07 .08 .09
-3.9 .00005 .00005 .00004 .00004 .00004 .00004 .00004 .00004 .00003 .00003
-3.8 .00007 .00007 .00007 .00006 .00006 .00006 .00006 .00005 .00005 .00005
-3.7 .00011 .00010 .00010 .00010 .00009 .00009 .00008 .00008 .00008 .00008
-3.6 .00016 .00015 .00015 .00014 .00014 .00013 .00013 .00012 .00012 .00011
-3.5 .00023 .00022 .00022 .00021 .00020 .00019 .00019 .00018 .00017 .00017
-3.4 · .00034 .00032 .00031 .00030 .00029 .00028 .00027 .00026 .00025 .00024
-3.3 .00048 .00047 .00045 .00043 .00042 .00040 .00039 .00038 .00036 .00035
-3.2 .00069 .00066 .00064 .00062 .00060 .00058 .00056 .00054 .00052 .00050
-3.1 .00097 .00094 .00090 .00087 .00084 .00082 .00079 .00076 .00074 .00071
-3.0 .00135 .00131 .00126 .00122 .00118 .00114 .00111 .00107 .00104 .00100
-2.9 .00187 .00181 .00175 .00169 .00164 .00159 .00154 .00149 .00144 .00139
-2.8 .00256 .00248 .00240 .00233 .00226 .00219 .00212 .00205 .00199 .00193
”2.7 .00347 .00336 .00326 .00317 .00307 .00298 .00289 .00280 .00272 .00264
-2.6 .00466 .00453 .00440 .00427 .00415 .00402 .00391 .00379 .00368 .00357
-2.5 .00621 .00604 .00587 .00570 .00554 .00539 .00523 .00508 .00494 .00480
-2.4 .00820 .00798 .00776 .00755 .00734 .00714 .00695 .00676 .00657 .00639
-2.3 .01072 .01044 .01017 .00990 .00964 .00939 .00914 .00889 .00866 .00842
-2.2 .01390 .01355 .01321 .01287 .01255 .01222 .01191 .01160 .01130 .01101
-2.1 .01786 .01743 .01700 .01659 .01618 .01578 .01539 .01500 .01463 .01426
-2.0 .02275 .02222 .02169 .02118 .02068 .02018 .01970 .01923 .01876 .01831
-1.9 .02872 .02807 .02743 .02680 .02619 .02559 .02500 .02442 .02385 .02330
-1.8 .03593 .03515 .03438 .03362 .03288 .03216 .03144 .03074 .03005 .02938
-1.7 .04457 .04363 .04272 .04182 .04093 .04006 .03920 .03836 .03754 .03673
-1.6 .05480 .05370 .05262 .05155 .05050 .04947 .04846 .04746 .04648 .04551
.06552 .06426
”1.5 .06681 .06301 .06178 .06057 .05938 .05821 .05705 .05592
-1.4 .08076 .07927 .07780 .07636 .07493 .07353 .07215 .07078 .06944 .06811
-1.3 .09680 .09510 .09342 .09176 .09012 .08851 .08691 .08534 .08379 .08226
-1.2 .11507 .11314 .11123 .10935 .10749 .10565 .10383 .10204 .10027 .09853
-1.1 .13567 .13350 .13136 .12924 .12714 .12507 .12302 .12100 .11900 .11702
-1.0 .15866 .15625 .15386 .15151 .14917 .14686 .14457 .14231 .14007 .13786
-0.9 .18406 .18141 .17879 .17619 .17361 .17106 .16853 .16602 .16354 .16109
-0.8 .21186 .20897 .20611 .20327 .20045 .19766 .19489 .19215 .18943 .18673
-0.7 .24196 .23885 .23576 .23270 .22965 .22663 .22363 .22065 .21770 .21476

”。.6 .27425 .27093 .26763 .26435 .26109 .25785 .25463 .25143 .24825 .24510
-0.5 .30854 .30503 .30153 .29806 .29460 .29116 .28774 .28434 .28096 .27760
-0.4 .34458 .34090 .33724 .33360 .32997 .32636 .32276 .31918 .31561 .31207
-0.3 .38209 .37828 .37448 .37070 .36693 .36317 .35942 .35569 .35197 .34827
-0.2 .42074 .41683 .41294 .40905 .40517 .40129 .39743 .39358 .38974 .38591
-0.1 .46017 .45620 .45224 .44828 .44433 .44038 .43644 .43251 .42858 .42465
-0.0 .50000 .49601 .49202 .48803 .48405 .48006 .47608 .47210 .46812 .46414

(IMSE4110 - page 5 of 6)
STANDARD NORMAL DISTRIBUTION: Table Values Repr AREA to the LEFT of the Z
z .00 .01 .02 .03 .04 .05 .06 .o7 .08 .09
0.0 .50000 .50399 .50798 .51197 .51595 .51994 .52392 .52790 .53188 .53586
0.1 .53983 .54380 .54776 .55172 .55567 .55962 .56356 .56749 .57142 .57535
0.2 .57926 .58317 .58706 .59095 .59483 .59871 .60257 .60642 .61026 .61409
0.3 .61791 .62172 .62552 .62930 .63307 .63683 .64058 .64431 .64803 .65173
0.4 .65542 .65910 .66276 .66640 .67003 .67364 .67724 .68082 .68439 .68793
0.5 .69146 .69497 .69847 .70194 .70540 .70884 .71226 .71566 .71904 .72240
0.6 .72575 .72907 .73237 .73565 .73891 .74215 .74537 .74857 .75175 .75490
0.7 .75804 .76115 .76424 .76730 .77035 .77337 .77637 .77935 .78230 .78524
0.8 .78814 .79103 .79389 .79673 .79955 .80234 .80511 .80785 .81057 .81327
0.9 .81594 .81859 .82121 .82381 .82639 .82894 .83147 .83398 .83646 .83891
1.0 .84134 .84375 .84614 .84849 .85083 .85314 .85543 .85769 .85993 .86214
1.1 .86433 .86650 .86864 .87076 .87286 .87493 .87698 .87900 .88100 .88298
1.2 .88493 .88686 .88877 .89065 .89251 .89435 .89617 .89796 .89973 .90147
1.3 .90320 .90490 .90658 .90824 .90988 .91149 .91309 .91466 .91621 .91774
1.4 .91924 .92073 .92220 .92364 .92507 .92647 .92785 .92922 .93056 .93189
1.5 .93319 .93448 .93574 .93699 .93822 .93943 .94062 .94179 .94295 .94408
1.6 .94520 .94630 .94738 .94845 .94950 .95053 .95154 .95254 .95352 .95449
1.7 .95543 .95637 .95728 .95818 .95907 .95994 .96080 .96164 .96246 .96327
1.8 .96407 .96485 .96562 .96638 .96712 .96784 .96856 .96926 .96995 .97062
1.9 .97128 .97193 .97257 .97320 .97381 .97441 .97500 .97558 .97615 .97670
2.0 .97725 .97778 .97831 .97882 .97932 .97982 .98030 .98077 .98124 .98169
2.1 .98214 .98257 .98300 .98341 .98382 .98422 .98461 .98500 .98537 .98574
2.2 .98610 .98645 .98679 .98713 .98745 .98778 .98809 .98840 .98870 .98899
2.3 .98928 .98956 .98983 .99010 .99036 .99061 .99086 .99111 .99134 .99158
2.4 .99180 .99202 .99224 .99245 .99266 .99286 .99305 .99324 .99343 .99361
2.5 .99379 .99396 .99413 .99430 .99446 .99461 .99477 .99492 .99506 .99520
2.6 .99534 .99547 .99560 .99573 .99585 .99598 .99609 .99621 .99632 .99643
2.7 .99653 .99664 .99674 .99683 .99693 .99702 .99711 .99720 .99728 .99736
2.8 .99744 .99752 .99760 .99767 .99774 .99781 .99788 .99795 .99801 .99807
2.9 .99813 .99819 .99825 .99831 .99836 .99841 .99846 .99851 .99856 .99861
3.0 .99865 .99869 .99874 .99878 .99882 .99886 .99889 .99893 .99896 .99900
3.1 .99903 .99906 .99910 .99913 .99916 .99918 .99921 .99924 .99926 .99929
3.2 .99931 .99934 .99936 .99938 .99940 .99942 .99944 .99946 .99948 .99950
3.3 .99952 .99953 .99955 .99957 .99958 .99960 .99961 .99962 .99964 .99965
3.4 .99966 .99968 .99969 .99970 .99971 .99972 .99973 .99974 .99975 .99976
3.5 .99977 .99978 .99978 .99979 .99980 .99981 .99981 .99982 .99983 .99983
3.6 .99984 .99985 .99985 .99986 .99986 .99987 .99987 .99988 .99988 .99989
3.7 .99989 .99990 .99990 .99990 .99991 .99991 .99992 .99992 .99992 .99992
3.8 .99993 .99993 .99993 .99994 .99994 .99994 .99994 .99995 .99995 .99995
3.9 .99995 .99995 .99996 .99996 .99996 .99996 .99996 .99996 .99997 .99997

- End of Paper -
(IMSE4110 - page 6 of 6)