---

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

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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	330.0		90	#VALUE!	#VALUE!	0	0.34	0.11	0.26	0.08	0.30	0.09			-0.425905000229335	-1.24828598259905	-0.525905000229335	-1.34828598259906					Cena akcji	330
	1	336.6	0.02	89	#VALUE!	#VALUE!	1	0.41	0.15	0.32	0.11	0.37	0.12			-0.2309710395737	-1.057959234364	-0.330413932174875	-1.15740212696518					r - wolna od ryzyka	4.5%
	2	343.2	0.019607843137255	88	#VALUE!	#VALUE!	2	0.48	0.19	0.38	0.14	0.45	0.17			-0.037730563582424	-0.8694042813915	-0.136613210077033	-0.968286927886109					Odch. stand stopy zwrotu	0.2
	3	349.8	0.019230769230769	87	#VALUE!	#VALUE!	3	0.56	0.25	0.44	0.18	0.52	0.22			0.153955078955928	-0.682484716369177	0.055635870930911	-0.780803924394195					p =	40%
	4	356.4	0.018867924528302	86	#VALUE!	#VALUE!	4	0.63	0.31	0.49	0.23	0.60	0.28			0.344219445245113	-0.497069317051362	0.246466923254345	-0.59482183904213
	5	363.0	0.018518518518519	85	#VALUE!	#VALUE!	5	0.70	0.38	0.55	0.28	0.67	0.34			0.533191522805268	-0.313031526741812	0.436008991224513	-0.410214058322567					WIBOR2W	4.61%
	6	363.0	0	84	#VALUE!	#VALUE!	6	0.70	0.38	0.54	0.27	0.67	0.34			0.534486964411124	-0.316758224476089	0.437877786103195	-0.413367402784019					+ powyżej	2%
weekend	7	363.0	0	83	#VALUE!	#VALUE!	7	0.70	0.37	0.54	0.27	0.67	0.34			0.535816972744804	-0.320540845827653	0.439784570805551	-0.416573247766906					WIBOR2W+5%	6.61%
	8	369.6	0.018181818181818	82	#VALUE!	#VALUE!	8	0.77	0.45	0.58	0.32	0.74	0.41			0.725952718644005	-0.135610970483637	0.630500578222162	-0.23106311090548
	9	376.2	0.017857142857143	81	#VALUE!	#VALUE!	9	0.82	0.52	0.62	0.38	0.79	0.48			0.915086863675855	0.048221194110824	0.820218533870804	-0.046647135694228					Cena wykonania 1	350
	10	382.8	0.017543859649123	80	#VALUE!	#VALUE!	10	0.87	0.59	0.65	0.43	0.84	0.55			1.10334060188084	0.23107384785211	1.00905969772263	0.136792943693904					Cena wykonania 2	380
	11	389.4	0.017241379310345	79	#VALUE!	#VALUE!	11	0.90	0.66	0.67	0.48	0.88	0.63			1.29083244038641	0.413062371486226	1.1971426449027	0.319372576002525					Termin opcji (w dniach)	90
	12	396.0	0.016949152542373	78	#VALUE!	#VALUE!	12	0.93	0.72	0.69	0.52	0.92	0.69			1.47767858837838	0.594299707975198	1.38458365475325	0.501204774350072
	13	396.0	0	77	#VALUE!	#VALUE!	13	0.93	0.72	0.68	0.51	0.92	0.69			1.48529091976538	0.596194317015074	1.39279467359531	0.503698070844996
weekend	14	396.0	0	76	#VALUE!	#VALUE!	14	0.93	0.73	0.67	0.51	0.92	0.69			1.49306580520225	0.598138998325186	1.40117214685498	0.506245339977918
	15	402.6	0.016666666666667	75	#VALUE!	#VALUE!	15	0.95	0.78	0.68	0.55	0.94	0.75			1.68207816112212	0.781204931307811	1.59079106820459	0.689917838390283
	16	409.2	0.016393442622951	74	#VALUE!	#VALUE!	16	0.97	0.83	0.69	0.58	0.96	0.81			1.87073879911932	0.963799014364187	1.78006232906108	0.87312254430595
	17	415.8	0.016129032258065	73	#VALUE!	#VALUE!	17	0.98	0.87	0.69	0.60	0.98	0.85			2.05916345778735	1.14603288590985	1.96910175054664	1.05597117866914
	18	422.4	0.015873015873016	72	#VALUE!	#VALUE!	18	0.99	0.91	0.68	0.62	0.98	0.89			2.24746720505965	1.32801731506877	2.15802448595965	1.23857459596878
	19	429.0	0.015625	71	#VALUE!	#VALUE!	19	0.99	0.93	0.68	0.63	0.99	0.92			2.43576478515741	1.50986253607547	2.34694536786091	1.42104311877897
	20	429.0	0	70	#VALUE!	#VALUE!	20	0.99	0.94	0.67	0.62	0.99	0.92			2.45105410054358	1.51856171670103	2.36286239017476	1.43037000633221
weekend	21	429.0	0	69	#VALUE!	#VALUE!	21	0.99	0.94	0.66	0.62	0.99	0.93			2.46668938212665	1.52746411385448	2.37912987854956	1.43990461027739
	22	435.6	0.015384615384616	68	#VALUE!	#VALUE!	22	1.00	0.96	0.65	0.62	0.99	0.95			2.65832766024476	1.71222152878753	2.57140496150872	1.6252988300515
	23	442.2	0.015151515151515	67	#VALUE!	#VALUE!	23	1.00	0.97	0.64	0.62	1.00	0.96			2.85028897556457	1.89714850092372	2.76400778152761	1.81086730688676
	24	448.8	0.014925373134328	66	#VALUE!	#VALUE!	24	1.00	0.98	0.64	0.62	1.00	0.98			3.04269539063619	2.08236130092618	2.95706050677842	1.99672641706841
	25	455.4	0.014705882352941	65	#VALUE!	#VALUE!	25	1.00	0.99	0.63	0.62	1.00	0.99			3.2356704208438	2.26797734160284	3.15068676228392	2.18299368304296
	26	462.0	0.014492753623189	64	#VALUE!	#VALUE!	26	1.00	0.99	0.62	0.61	1.00	0.99			3.42933942593498	2.45411554767432	3.34501202166383	2.36978814340317
	27	462.0	0	63	#VALUE!	#VALUE!	27	1.00	0.99	0.61	0.60	1.00	0.99			3.45429119872634	2.47135792082553	3.37062519607293	2.38769191817212
weekend	28	462.0	0	62	#VALUE!	#VALUE!	28	1.00	0.99	0.60	0.59	1.00	0.99			3.47986156959912	2.48903311845735	3.39686223894587	2.40603378780409
	29	458.9	-0.00661	61	#VALUE!	#VALUE!	29	1.00	0.99	0.59	0.58	1.00	0.99			3.42552007542356	2.42660309455513	3.3431928151887	2.34427583432027
	30	455.9	-0.006653982826483	60	#VALUE!	#VALUE!	30	1.00	0.99	0.58	0.57	1.00	0.99			3.36997011739146	2.36276322690417	3.28832045929869	2.28111356881139
	31	452.8	-0.006698554895721	59	#VALUE!	#VALUE!	31	1.00	0.99	0.57	0.56	1.00	0.99			3.31316830144872	2.29746162406272	3.23220191610545	2.21649523871944
	32	449.8	-0.006743728128794	58	#VALUE!	#VALUE!	32	1.00	0.99	0.56	0.55	1.00	0.98			3.25506893198624	2.23064358243399	3.17479163479429	2.15036628524204
	33	446.7	-0.006789514770533	57	#VALUE!	#VALUE!	33	1.00	0.98	0.55	0.54	1.00	0.98			3.1956238459867	2.16225138027573	3.11604160341127	2.08266913770031
	34	446.7	0	56	#VALUE!	#VALUE!	34	1.00	0.99	0.54	0.53	1.00	0.98			3.22174099048085	2.17918281109447	3.14285992670619	2.10030174731981
weekend	35	446.7	0	55	#VALUE!	#VALUE!	35	1.00	0.99	0.53	0.52	1.00	0.98			3.24858793741004	2.19659465005931	3.17041434141298	2.11842105406225
	36	443.7	-0.006835927400589	54	#VALUE!	#VALUE!	36	1.00	0.98	0.52	0.51	1.00	0.98			3.18764404556851	2.1259547625833	3.11018437864436	2.04849509565915
	37	440.6	-0.006882978944957	53	#VALUE!	#VALUE!	37	1.00	0.98	0.51	0.50	1.00	0.98			3.12521943041121	2.05356101525831	3.04848033418973	1.97682191903684
	38	437.6	-0.006930682687972	52	#VALUE!	#VALUE!	38	1.00	0.98	0.50	0.49	1.00	0.97			3.06125455547571	1.97934080220627	2.9852428604691	1.90332910719966
	39	434.5	-0.006979052284821	51	#VALUE!	#VALUE!	39	1.00	0.97	0.49	0.48	1.00	0.97			2.99568630003615	1.90321704067859	2.92040903476524	1.82793977540768
	40	431.5	-0.007028101774569	50	#VALUE!	#VALUE!	40	1.00	0.97	0.48	0.46	1.00	0.96			2.9284476640149	1.82510779602585	2.85391206476491	1.75057219677586
	41	431.5	0	49	#VALUE!	#VALUE!	41	1.00	0.97	0.47	0.46	1.00	0.96			2.95573185882226	1.84119028366722	2.881945380085	1.76740380492996
weekend	42	431.5		48	#VALUE!	#VALUE!	42	1.00	0.97	0.46	0.45	1.00	0.96			2.9838896638344	1.85779812656652	2.91085998950038	1.78476845223249
																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	291.6		90	#VALUE!	#VALUE!	0
	1	298.2	0.022635666546632	89	#VALUE!	#VALUE!	1									WIBOR2W	5.54%
	2	304.8	0.022134634344479	88	#VALUE!	#VALUE!	2									dadatkowo	5%
	3	311.4	0.021655302149774	87	#VALUE!	#VALUE!	3									WIBOR2W+5%	10.54%
	4	318.0	0.02119629008356	86	#VALUE!	#VALUE!	4
	5	324.6	0.020756332831787	85	#VALUE!	#VALUE!	5									strike price A	230
	6	324.6	0	84	#VALUE!	#VALUE!	6									strike price B	250
weekend	7	324.6	0	83	#VALUE!	#VALUE!	7									maturity (w dniach)	90
	8	331.2	0.020334267997343	82	#VALUE!	#VALUE!	8
	9	337.8	0.019929025844887	81	#VALUE!	#VALUE!	9
	10	344.4	0.019539620247966	80	#VALUE!	#VALUE!	10
	11	351.0	0.019165140677136	79	#VALUE!	#VALUE!	11									dywidenda	10%
	12	357.6	0.018804745092049	78	#VALUE!	#VALUE!	12									ustalenie prawa w t=15	16
	13	357.6	0	77	#VALUE!	#VALUE!	13									wypłata w t=16
weekend	14	357.6	0	76	#VALUE!	#VALUE!	14
	15	364.2	0.018457653620715	75	#VALUE!	#VALUE!	15
	16	370.8	0.018123142926067	74	#VALUE!	#VALUE!	16	wys dyw				37.0775244157417
	17	401.0	0.081450961130453	73	#VALUE!	#VALUE!	17
	18	407.6	0.016459869022261	72	#VALUE!	#VALUE!	18	payment				370.5
	19	414.2	0.01619332894873	71	#VALUE!	#VALUE!	19
	20	414.2	0	70	#VALUE!	#VALUE!	20
weekend	21	414.2	0	69	#VALUE!	#VALUE!	21									291.575244157417						-91.5752441574167
	22	420.8	0.015935283658556	68	#VALUE!	#VALUE!	22
	23	427.4	0.01568533342121	67	#VALUE!	#VALUE!	23
	24	434.0	0.015443103198483	66	#VALUE!	#VALUE!	24							Sd=200-wartość dyw/(1+rf)^dzień dyw/360
	25	440.6	0.015208240766854	65	#VALUE!	#VALUE!	25
	26	447.2	0.014980415008615	64	#VALUE!	#VALUE!	26
	27	447.2	0	63	#VALUE!	#VALUE!	27
weekend	28	447.2	0	62	#VALUE!	#VALUE!	28
	29	444.1	-0.006829134751755	61	#VALUE!	#VALUE!	29
	30	441.1	-0.006876092514099	60	#VALUE!	#VALUE!	30
	31	438.0	-0.006923700519411	59	#VALUE!	#VALUE!	31
	32	435.0	-0.006971972368117	58	#VALUE!	#VALUE!	32
	33	431.9	-0.007020922042597	57	#VALUE!	#VALUE!	33
	34	431.9	0	56	#VALUE!	#VALUE!	34
weekend	35	431.9	0	55	#VALUE!	#VALUE!	35
	36	428.9	-0.007070563920681	54	#VALUE!	#VALUE!	36
	37	425.8	-0.007120912789735	53	#VALUE!	#VALUE!	37
	38	422.7	-0.007171983861341	52	#VALUE!	#VALUE!	38
	39	419.7	-0.007223792786624	51	#VALUE!	#VALUE!	39
	40	416.6	-0.007276355672242	50	#VALUE!	#VALUE!	40
	41	416.6	0	49	#VALUE!	#VALUE!	41
weekend	42	417.6		48	#VALUE!	#VALUE!	42

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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

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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