---

Overview

55
56
57
58
Arkusz1
59
60
61

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Sheet 1: 55

Futures. Marking-to-market
Problem 55
Tri-Mark receives a $1200,000 from a major contract on December 18. These funds
are not needed for six days and, rather than putting them into short-term marketable
securities Tri-Mark's Chief Financial Officer (CFO) wants to use these funds to
speculate in pork bellies. He purchases 55 contracts. Traded on the
Chicago Mercantile Exchange (CME), each pork belly futures contract is for
40,000 pounds and requires a $2,150 initial margin and $1,800 maintenance margin.
The current futures price for February delivery is $0,5380. The contracts are
purchased at this price.
(a) What is the initial value of Tri-Mark's margin account ?
(b) Immediately after the CFO purchases the contracts, the government issues
a major report on dietary fat that is expected to reduce the public's bacon
consumption. On succeeding days after the purchase of the contracts, pork
belly futures trade at $0,5312, $0,5300, $0,5120, $0,4998, $0,4887, and $0,4880.
Compute the changes in the margin account on each of these days.
Assuming that Tri-Mark closes its position at the end of sixth day, what
is its profit/loss on its speculation ?

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Sheet 2: 56

Futures & Options
Problem 56
A distributor has just purchased DM 375 000 worth of fine German beer for
the central Ohio market and must pay for the beer in 90 days. The distributor
is concerned about changes in the value of the German mark during that
period. It has accumulated the following information:
Today's spot exchange rate: So ($/DM) = 0,5019
Exchange rate available on three-month futures contract: F1,4 ($/DM) = 0,5028
Distributor's estimate of the spot exchange rate in three months: S1,4 ($/DM) = 0,5050
	Option information			Call option	Put option
	Contract size		DM	62,500.000	62,500.000
	Exercise price		$/DM	0.5050	0.5060
	Premium		$/DM	0.0010	0.0012
(a) If the distributor remains unhedged, how much will he expect to pay
in dollars for the beer ? Draw the payoff pattern.
(b) If currency futures contracts are used to hedge (each contract is for DM
125 000), how much will the distributor pay in dollars for the beer ? Draw								$	189375
the payoff pattern for the futures contract and for the hedged position.
(c) If the distributor hedges this exposure with an option, which type of option									188550
should he use ? Assuming that the distributor's estimate of the future spot
rate is accurate, should the distributor exercise this option ? If the distributor
exercises the option, how many dollars will he pay for the beer ? Draw
the payoff pattern for the option contract and for the hedged position.
(d) Given your answers to the above questions, which is the better way to
hedge the distributor's currency risk ?

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Sheet 3: 57

Option characterictics
Problem 57
A firm is thinking of purchasing a put option on the DM. The option has
an exercise price of $0,5000 and a premium of $0,05. The current spot
rate is $0,5300.
(a) Draw the payoff diagram for the option, labelling all of its parts.
(b) Is the option in or out of the money ? By how much ?
(c) What is the intrinsic value of the option ?
(d) What is the time value of the option ?
				0	1	2	3	4	5	6	7	8
					-400	120	120	120	120	120	120	120
			280,347.44 zł			112,138.97 zł
			-495,238.10 zł		-520	-297,142.86 zł
						-185,003.88 zł

---

Sheet 4: 58

Call or Put Option
Problem 58
A person interested in speculating in the DM has gathered the following
information:
Today's spot exchange rate: So ($/DM) = 0,5019.
Estimate of the spot exchange rate in six months: S1/2 ($/DM) = 0,5045.
	Option information		Call option	Put option
	Contract size	DM	62.500	62.500
	Exercise price	$/DM	0.5050	0.5060
	Premium	$/DM	0.0010	0.0012
Should he buy a call option or a put option? What will the profits in dollars
be from this strategy if one DM option contract is purchased?

---

Sheet 5: Arkusz1

	Dzień	Cena akcji	stopa zwrotu z akcji	okres opcji	Cena rozl. 350	Cena rozl. 380	Dzień	DELTA (350)	DELTA (380)	RHO (350)	RHO (380)	RHO (350)	RHO (380)			D1(1)	D1(2)	D2(1)	D2(2)					Parametry
	0	24.0		90	#VALUE!	#VALUE!	0	0.26	0.08	0.01	0.00	0.23	0.07			-0.645227076735364	-1.38630679827258	-0.745227076735364	-1.48630679827258					Cena akcji	24
	1	24.5	0.02	89	#VALUE!	#VALUE!	1	0.33	0.12	0.02	0.01	0.29	0.10			-0.451440255281457	-1.19667171642709	-0.550883147882633	-1.29611460902826					r - wolna od ryzyka	4.2%
	2	25.0	0.019607843137255	88	#VALUE!	#VALUE!	2	0.40	0.16	0.02	0.01	0.36	0.13			-0.259366879005835	-1.00882064850787	-0.358249525500443	-1.10770329500248					Odch. stand stopy zwrotu	0.2
	3	25.4	0.019230769230769	87	#VALUE!	#VALUE!	3	0.47	0.21	0.03	0.01	0.43	0.18			-0.068868871290857	-0.822617539962649	-0.167188079315875	-0.920936747987667					p =	40%
	4	25.9	0.018867924528302	86	#VALUE!	#VALUE!	4	0.55	0.26	0.03	0.01	0.51	0.23			0.120186727109954	-0.637931535667152	0.022434205119186	-0.73568405765792
	5	26.4	0.018518518518519	85	#VALUE!	#VALUE!	5	0.62	0.32	0.04	0.02	0.58	0.29			0.307928281161307	-0.454636461167318	0.210745749580552	-0.551818992748073					WIBOR2W	4.61%
	6	26.4	0	84	#VALUE!	#VALUE!	6	0.62	0.32	0.04	0.02	0.58	0.29			0.307970795169053	-0.459119593670733	0.211361616861124	-0.555728771978662					+ powyżej	2%
weekend	7	26.4	0	83	#VALUE!	#VALUE!	7	0.62	0.32	0.03	0.02	0.58	0.29			0.30802479603071	-0.463672783715347	0.211992394091457	-0.5597051856546					WIBOR2W+5%	6.61%
	8	26.9	0.018181818181818	82	#VALUE!	#VALUE!	8	0.69	0.39	0.04	0.02	0.66	0.35			0.496860749987526	-0.279528043665588	0.401408609565683	-0.37498018408743
	9	27.4	0.017857142857143	81	#VALUE!	#VALUE!	9	0.75	0.46	0.04	0.02	0.72	0.42			0.684670583600906	-0.096496032339411	0.589802253795854	-0.191364362144462					Cena wykonania 1	26
	10	27.8	0.017543859649123	80	#VALUE!	#VALUE!	10	0.81	0.53	0.04	0.03	0.78	0.50			0.871574723789283	0.085540979041075	0.777293819631077	-0.008739925117132					Cena wykonania 2	28
	11	28.3	0.017241379310345	79	#VALUE!	#VALUE!	11	0.85	0.61	0.05	0.03	0.83	0.57			1.0576908766162	0.266697879234598	0.964001081132496	0.173008083750896					Termin opcji (w dniach)	90
	12	28.8	0.016949152542373	78	#VALUE!	#VALUE!	12	0.89	0.67	0.05	0.04	0.87	0.64			1.24313441430769	0.447087097144989	1.15003948068257	0.353992163519862
	13	28.8	0	77	#VALUE!	#VALUE!	13	0.89	0.67	0.05	0.04	0.88	0.64			1.24931633582362	0.448116555051371	1.15682008965354	0.355620308881294
weekend	14	28.8	0	76	#VALUE!	#VALUE!	14	0.90	0.67	0.05	0.03	0.88	0.64			1.25563209663669	0.449178490516602	1.16373843828942	0.357284832169333
	15	29.3	0.016666666666667	75	#VALUE!	#VALUE!	15	0.93	0.74	0.05	0.04	0.91	0.71			1.44315565535626	0.631343494565093	1.35186856243873	0.540056401647566
	16	29.8	0.016393442622951	74	#VALUE!	#VALUE!	16	0.95	0.79	0.05	0.04	0.94	0.76			1.63029682052417	0.813017849407117	1.53962035046594	0.722341379348881
	17	30.2	0.016129032258065	73	#VALUE!	#VALUE!	17	0.97	0.84	0.05	0.04	0.96	0.82			1.81717027967154	0.994312547742776	1.72710857243083	0.904250840502067
	18	30.7	0.015873015873016	72	#VALUE!	#VALUE!	18	0.98	0.88	0.05	0.04	0.97	0.86			2.00388999866627	1.17533768161435	1.91444727956628	1.08589496251436
	19	31.2	0.015625	71	#VALUE!	#VALUE!	19	0.99	0.91	0.05	0.05	0.98	0.90			2.19056956543655	1.35620277482435	2.10175014814006	1.26738335752786
	20	31.2	0	70	#VALUE!	#VALUE!	20	0.99	0.91	0.05	0.05	0.98	0.90			2.20420566844788	1.36390024922196	2.11601395807906	1.27570853885314
weekend	21	31.2	0	69	#VALUE!	#VALUE!	21	0.99	0.91	0.05	0.04	0.98	0.90			2.21815126315353	1.37177857799465	2.13059175957644	1.28421907441756
	22	31.7	0.015384615384615	68	#VALUE!	#VALUE!	22	0.99	0.94	0.05	0.05	0.99	0.93			2.40806203892275	1.55548873837705	2.32113934018672	1.46856603964101
	23	32.2	0.015151515151515	67	#VALUE!	#VALUE!	23	1.00	0.96	0.05	0.05	0.99	0.95			2.59825662555175	1.73934440277964	2.51197543151479	1.65306320874268
	24	32.6	0.014925373134328	66	#VALUE!	#VALUE!	24	1.00	0.97	0.05	0.05	1.00	0.97			2.78885560006625	1.92346092893189	2.70322071620848	1.83782604507412
	25	33.1	0.014705882352941	65	#VALUE!	#VALUE!	25	1.00	0.98	0.05	0.05	1.00	0.98			2.97998091251891	2.10795476761594	2.89499725395903	2.02297110905606
	26	33.6	0.014492753623188	64	#VALUE!	#VALUE!	26	1.00	0.99	0.05	0.05	1.00	0.99			3.1717562719241	2.29294382899124	3.08742886765295	2.20861642472009
	27	33.6	0	63	#VALUE!	#VALUE!	27	1.00	0.99	0.05	0.04	1.00	0.99			3.19476872888214	2.30900904390329	3.11110272622873	2.22534304124988
weekend	28	33.6	0	62	#VALUE!	#VALUE!	28	1.00	0.99	0.04	0.04	1.00	0.99			3.2183522734559	2.32547793856134	3.13535294280265	2.24247860790808
	29	33.4	-0.00661	61	#VALUE!	#VALUE!	29	1.00	0.99	0.04	0.04	1.00	0.99			3.16197449688146	2.26181127096683	3.07964723664661	2.17948401073197
	30	33.2	-0.006653982826483	60	#VALUE!	#VALUE!	30	1.00	0.99	0.04	0.04	1.00	0.98			3.10433674152813	2.19670315328312	3.02268708343536	2.11505349519034
	31	32.9	-0.006698554895721	59	#VALUE!	#VALUE!	31	1.00	0.98	0.04	0.04	1.00	0.98			3.04539343272711	2.1301003535125	2.96442704738384	2.04913396816923
	32	32.7	-0.006743728128794	58	#VALUE!	#VALUE!	32	1.00	0.98	0.04	0.04	1.00	0.98			2.98509656304579	2.06194674677177	2.90481926585384	1.98166944957982
	33	32.5	-0.006789514770533	57	#VALUE!	#VALUE!	33	1.00	0.98	0.04	0.04	1.00	0.97			2.92339551611267	1.99218310294791	2.84381327353725	1.91260086037249
	34	32.5	0	56	#VALUE!	#VALUE!	34	1.00	0.98	0.04	0.04	1.00	0.97			2.94719563274213	2.00770561311682	2.86831456896746	1.92882454934216
weekend	35	32.5	0	55	#VALUE!	#VALUE!	35	1.00	0.98	0.04	0.04	1.00	0.97			2.97166171333651	2.0236693482864	2.89348811733945	1.94549575228935
	36	32.3	-0.00683592740059	54	#VALUE!	#VALUE!	36	1.00	0.97	0.04	0.04	1.00	0.97			2.90827016610432	1.95154035952909	2.83081049918017	1.87408069260494
	37	32.0	-0.006882978944957	53	#VALUE!	#VALUE!	37	1.00	0.97	0.04	0.04	1.00	0.96			2.84332796172542	1.87761457959436	2.76658886550394	1.80087548337288
	38	31.8	-0.006930682687973	52	#VALUE!	#VALUE!	38	1.00	0.96	0.04	0.04	1.00	0.96			2.7767722080356	1.80181733895555	2.70076051302899	1.72580564394894
	39	31.6	-0.006979052284821	51	#VALUE!	#VALUE!	39	1.00	0.96	0.04	0.03	1.00	0.95			2.70853619914608	1.72406934999817	2.63325893387517	1.64879208472726
	40	31.4	-0.007028101774569	50	#VALUE!	#VALUE!	40	1.00	0.95	0.04	0.03	0.99	0.94			2.63854909979076	1.64428631932845	2.56401350054076	1.56975072007846
	41	31.4	0	49	#VALUE!	#VALUE!	41	1.00	0.95	0.04	0.03	1.00	0.94			2.66300001330406	1.65864293566651	2.5892135345668	1.58485645692925
weekend	42	31.4		48	#VALUE!	#VALUE!	42	1.00	0.95	0.03	0.03	1.00	0.95			2.68823531262942	1.67347011164046	2.6152056382954	1.60044043730644
																INPUTS
																cena akcji	200
																r - wolna od ryzyka	7%
												odch. standardowe stopy zwrotu akcji					0.2
	Dzień	Cena akcji	stopa zwrotu z akcji	okres opcji	Cena rozl. 350	Cena rozl. 380	Dzień									p =	30%
	0	-14.4		90	#VALUE!	#VALUE!	0
	1	-13.9	-0.033265105766922	89	#VALUE!	#VALUE!	1									WIBOR2W	5.54%
	2	-13.5	-0.034409749731142	88	#VALUE!	#VALUE!	2									dadatkowo	5%
	3	-13.0	-0.035635974702065	87	#VALUE!	#VALUE!	3									WIBOR2W+5%	10.54%
	4	-12.5	-0.036952824625593	86	#VALUE!	#VALUE!	4
	5	-12.0	-0.038370731538905	85	#VALUE!	#VALUE!	5									strike price A	230
	6	-12.0	0	84	#VALUE!	#VALUE!	6									strike price B	250
weekend	7	-12.0	0	83	#VALUE!	#VALUE!	7									maturity (w dniach)	90
	8	-11.5	-0.039901792507117	82	#VALUE!	#VALUE!	8
	9	-11.1	-0.04156011561704	81	#VALUE!	#VALUE!	9
	10	-10.6	-0.043362255989374	80	#VALUE!	#VALUE!	10
	11	-10.1	-0.045327770371657	79	#VALUE!	#VALUE!	11									dywidenda	10%
	12	-9.6	-0.047479929723423	78	#VALUE!	#VALUE!	12									ustalenie prawa w t=15	16
	13	-9.6	0	77	#VALUE!	#VALUE!	13									wypłata w t=16
weekend	14	-9.6	0	76	#VALUE!	#VALUE!	14
	15	-9.1	-0.049846644921232	75	#VALUE!	#VALUE!	15
	16	-8.7	-0.052461683847971	74	#VALUE!	#VALUE!	16	wys dyw				-0.866953476123626
	17	15.4	-2.77754235529084	73	#VALUE!	#VALUE!	17
	18	15.9	0.031147664432129	72	#VALUE!	#VALUE!	18	payment				16.8
	19	16.4	0.03020679336871	71	#VALUE!	#VALUE!	19
	20	16.4	0	70	#VALUE!	#VALUE!	20
weekend	21	16.4	0	69	#VALUE!	#VALUE!	21									-14.4295347612363						214.429534761236
	22	16.9	0.029321097048812	68	#VALUE!	#VALUE!	22
	23	17.3	0.028485860372317	67	#VALUE!	#VALUE!	23
	24	17.8	0.027696890613552	66	#VALUE!	#VALUE!	24							Sd=200-wartość dyw/(1+rf)^dzień dyw/360
	25	18.3	0.026950447030171	65	#VALUE!	#VALUE!	25
	26	18.8	0.026243181555749	64	#VALUE!	#VALUE!	26
	27	18.8	0	63	#VALUE!	#VALUE!	27
weekend	28	18.8	0	62	#VALUE!	#VALUE!	28
	29	18.5	-0.01183220539155	61	#VALUE!	#VALUE!	29
	30	18.3	-0.011973882832559	60	#VALUE!	#VALUE!	30
	31	18.1	-0.012118994249754	59	#VALUE!	#VALUE!	31
	32	17.9	-0.012267666023754	58	#VALUE!	#VALUE!	32
	33	17.7	-0.012420030813782	57	#VALUE!	#VALUE!	33
	34	17.7	0	56	#VALUE!	#VALUE!	34
weekend	35	17.7	0	55	#VALUE!	#VALUE!	35
	36	17.4	-0.012576227952473	54	#VALUE!	#VALUE!	36
	37	17.2	-0.012736403870848	53	#VALUE!	#VALUE!	37
	38	17.0	-0.012900712556185	52	#VALUE!	#VALUE!	38
	39	16.8	-0.013069316045798	51	#VALUE!	#VALUE!	39
	40	16.5	-0.013242384960041	50	#VALUE!	#VALUE!	40
	41	16.5	0	49	#VALUE!	#VALUE!	41
weekend	42	17.5		48	#VALUE!	#VALUE!	42

---

Sheet 6: 59

Black-Scholes Model. Put-Call Parity
Problem 59
Consider a call option on the stock of Arkla Natural Gas. The stock currently
trades for $22,75 per share. The option has one month to expiration and an
exercise price of $20,00. The riskless interest rate is 5% (annually) and the variance
is 0,45.
(a) What is the value of the call option?
(b) The price exceeds $2,75. Why?
(c) Suppose the risk-free rate was 7% instead of 5%. Find the option's value
Is this result consistent with your expectation ?
							#VALUE!
							-90	110
					10.00 zł
				2.9999999985
							42
							84
									26.6666666666667

---

Sheet 7: 60

Swap terminology
Problem 60
Gettman Inc., a manufacturer of sports footwear, recently negotiated
a ten-year, $5 million bank loan with Texas Commerce Bank (TCB). The loan
requires semiannual payments based on a floating-rate index of six-month
LIBOR + 1%. Furthermore, the loan contains a covenant stipulating that
Gettman should hedge within the next 60 days, to the degree possible,
the interest rate risk in the loan. The CFO of Gettman decides to achive this
objective by entering into an interest swap, where the firm will receive floating
and pay fixed. The swap dealer quotes ten year swaps at "80-87". The current
ten-year Treasury bond yield is 7%.
(a) What is the percentage coupon (as a function of LIBOR, on a 365-day
basis) received by TCB on this loan?
(b) What is the fixed rate paid by Gettman Inc. to the dealer?
(c) What is the floating rate paid by the dealer to the firm?
(d) What is the net interest cost for Gettman on its borrowed funds?
(e) Can you offer a plausible reason why TCB may want the firm to hedge the
interest rate risk when presumably the bank itself could have provided a
fixed-rate loan to the firm?

---

Sheet 8: 61

Swap. Economic value

Problem 61

Consider a five-year, semiannual settlement, $100 million notional principal

8%-versus-LIBOR interest rate swap between Firm X (the fixed payer) and

Firm Y (the fixed receiver). Also suppose that just after the sixth payment (i.e.,

after three years), Firm X falls into financial troubles and files for Chapter 7.

(a) What is the loss per period to Firm Y if the market today offers swaps for a

fixed rate 7,2% against LIBOR flat?

(b) What is the economic value of the swap?

(c) If instead the market today offers swaps for a fixed rate of 8,4% against the

LIBOR, what is the loss to Firm Y? What is the economic value of the swap

in this case?

722,570.16 zł

-200000

#VALUE!

ex 72

8000000

7200000

4400000

because we are calculating it per period