dont commit my question if you know you will flag for honor code violation

Hello can anyone please help me in those derivatives questions. I really cant figure out how to do them

Part A A portfolio contains two separate options: P1(K1) and C2(K2). The portfolio is short in P1(K1) and long in C2(K2). Assume that the two European options described above are for the same underlying assets and have the same maturity (T) and have no interim cash flows (i.e. no dividends). Assume that each of the options has a different strike (Ki) such that K1 K2 P1 -max(0,K1-S)= K1-S -max(0,K1-S)= 0 -max(0,K1-S)= 0 C2 Total max(0,S-K2)=0 S-K_1 max(0,S-K2)=0 max(0,S-K2)=S-K2 S-K2 0 40 100 S P1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 140 P2 100 99 98 97 96 95 94 93 92 91 90 89 88 87 86 85 84 83 82 81 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 -140 -139 -138 -137 -136 -135 -134 -133 -132 -131 -130 -129 -128 -127 -126 -125 -124 -123 -122 -121 -120 -119 -118 -117 -116 -115 -114 -113 -112 -111 -110 -109 -108 -107 -106 -105 -104 -103 -102 -101 -100 -99 -98 -97 -96 -95 -94 180 C3 Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 T 30 20 10 0 -10 -20 -30 -40 -50 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 -93 -92 -91 -90 -89 -88 -87 -86 -85 -84 -83 -82 -81 -80 -79 -78 -77 -76 -75 -74 -73 -72 -71 -70 -69 -68 -67 -66 -65 -64 -63 -62 -61 -60 -59 -58 -57 -56 -55 -54 -53 -52 -51 -50 -49 -48 -47 -46 -45 -44 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 -40 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 3 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -40 -40 -40 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0 0 0 0 0 0 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 197 198 199 200 0 0 0 0 0 0 0 0 17 18 19 20 17 18 19 20 Total Total Dervatives Project September 2017 Part A Payoff for P1 (K1 ) Since the portfolio is short in option P1 (K1 ), it follows that the payoff is: P1 (K1 ) Payoff = max (0, K1 S) (1) where S denotes the underlying asset price. Payoff for C2 (K2 ) Since the portfolio is long in option C2 (K2 ), it follows that the payoff is: C2 (K2 ) Payoff = max (0, S K2 ) (2) where K1 S0 (1 + i)T , it follows that the arbitrageur would make a risk-free trading profit equal to Forward price S0 (1 + i)T . Arbitrageurs would increase the demand for short positions of such a forward contract, thereby exerting a downward pressure on the forward price. It can be shown that when the forward price is less than S0 (1 + i)T , the action of arbitrageurs would exert an upward pressure on the forward price. Equilibrium is attained when Equation 8 is satisfied. Why Futures may Have Less Risk The counter-party to every futures trade is the clearinghouse. In virtually all cases, clearinghouses have a high creditworthiness. This makes the default risk inherent in futures contracts to be negligible. Each party to a futures trade is compelled to post a margin, which acts as collateral. The position of a trader is marked-to-market daily, with the profit/loss being posted to the margin account. If the margin account drops below the maintenance margin, the party receives a margin call, which requires him/her to top-up the margin account. Failure to top-up the margin account results in the futures contract being closed out. In summary, it is the mechanism of running a margin account and marking to market on a daily basis that significantly reduces the risk involved in futures. Unlike forwards, which are private transactions, futures markets tend to be regulated. The regulator would seek to protect the interests of the traders in the futures contracts. 3 100 S 100 50 0 -50 -100 -150 P1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -100 -99 -98 -97 -96 Total -95 -94 -93 -92 -91 -90 -89 -88 -87 -86 -85 -84 -83 Total -82 -81 -80 -79 -78 -77 -76 -75 -74 -73 -72 -71 -70 -69 -68 -67 -66 -65 -64 -63 -62 -61 -60 -59 -58 -57 -56 -55 -54 120 C2 Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -100 -99 -98 -97 -96 -95 -94 -93 -92 -91 -90 -89 -88 -87 -86 -85 -84 -83 -82 -81 -80 -79 -78 -77 -76 -75 -74 -73 -72 -71 -70 -69 -68 -67 -66 -65 -64 -63 -62 -61 -60 -59 -58 -57 -56 -55 -54 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 -53 -52 -51 -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -53 -52 -51 -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 197 198 199 200 0 0 0 0 77 78 79 80 77 78 79 80 Share Price Range S K2 P1 -max(0,K1-S)= K1-S -max(0,K1-S)= 0 -max(0,K1-S)= 0 C2 Total max(0,S-K2)=0 S-K_1 max(0,S-K2)=0 max(0,S-K2)=S-K2 S-K2 0 This sheet demonstrates Part B of the solution with the aid of a numerical example Inputs K1 K3 - K2 = K2 - K1 Payoff Table $ $ 100.00 20.00 ... Strikes equally spaced apart. Strike Values K1 K2 K3 $ $ $ 100.00 120.00 140.00 Notes .... Ideally, set input in cell C6 in a range between 5 to 40 for a better plot, given that K1 is set at a 100. ... The plot range for this illustration is where the share price is between 0 to 200 Share Price $0.00 $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00 $11.00 $12.00 $13.00 $14.00 $15.00 $16.00 $17.00 $18.00 $19.00 $20.00 $21.00 $22.00 $23.00 $24.00 $25.00 $26.00 $27.00 $28.00 $29.00 $30.00 $31.00 $32.00 $33.00 $34.00 $35.00 $36.00 $37.00 $38.00 $39.00 $40.00 $41.00 $42.00 $43.00 $44.00 $45.00 $46.00 $47.00 $48.00 $49.00 $50.00 $51.00 $52.00 $53.00 $54.00 $55.00 $56.00 $57.00 $58.00 $59.00 $60.00 $61.00 $62.00 $63.00 $64.00 $65.00 $66.00 $67.00 $68.00 $69.00 $70.00 $71.00 $72.00 $73.00 $74.00 $75.00 $76.00 $77.00 $78.00 $79.00 $80.00 $81.00 $82.00 $83.00 $84.00 $85.00 $86.00 $87.00 $88.00 $89.00 $90.00 $91.00 $92.00 $93.00 $94.00 $95.00 $96.00 $97.00 $98.00 $99.00 $100.00 $101.00 $102.00 $103.00 $104.00 $105.00 $106.00 $107.00 $108.00 $109.00 $110.00 $111.00 $112.00 $113.00 $114.00 $115.00 $116.00 $117.00 $118.00 $119.00 $120.00 $121.00 $122.00 $123.00 $124.00 $125.00 $126.00 $127.00 $128.00 $129.00 $130.00 $131.00 $132.00 $133.00 $134.00 $135.00 $136.00 $137.00 $138.00 $139.00 $140.00 $141.00 $142.00 $143.00 $144.00 $145.00 $146.00 $147.00 $148.00 $149.00 $150.00 $151.00 $152.00 $153.00 $154.00 $155.00 $156.00 $157.00 $158.00 $159.00 $160.00 $161.00 $162.00 $163.00 $164.00 $165.00 $166.00 $167.00 $168.00 $169.00 $170.00 $171.00 $172.00 $173.00 $174.00 $175.00 $176.00 $177.00 $178.00 $179.00 $180.00 $181.00 $182.00 $183.00 $184.00 $185.00 $186.00 $187.00 $188.00 $189.00 $190.00 $191.00 $192.00 $193.00 $194.00 $195.00 $196.00 $197.00 $198.00 $199.00 $200.00 Plot of Portfolio Payoff C3(K3) $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Total Portfolio Payoff -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 Total Portfolio Payof $70 $60 Total Portfolio Payof $50 $40 Payoff P1(K1) $100.00 $99.00 $98.00 $97.00 $96.00 $95.00 $94.00 $93.00 $92.00 $91.00 $90.00 $89.00 $88.00 $87.00 $86.00 $85.00 $84.00 $83.00 $82.00 $81.00 $80.00 $79.00 $78.00 $77.00 $76.00 $75.00 $74.00 $73.00 $72.00 $71.00 $70.00 $69.00 $68.00 $67.00 $66.00 $65.00 $64.00 $63.00 $62.00 $61.00 $60.00 $59.00 $58.00 $57.00 Payoff P2(K2) -$120.00 -$119.00 -$118.00 -$117.00 -$116.00 -$115.00 -$114.00 -$113.00 -$112.00 -$111.00 -$110.00 -$109.00 -$108.00 -$107.00 -$106.00 -$105.00 -$104.00 -$103.00 -$102.00 -$101.00 -$100.00 -$99.00 -$98.00 -$97.00 -$96.00 -$95.00 -$94.00 -$93.00 -$92.00 -$91.00 -$90.00 -$89.00 -$88.00 -$87.00 -$86.00 -$85.00 -$84.00 -$83.00 -$82.00 -$81.00 -$80.00 -$79.00 -$78.00 -$77.00 $30 $20 $10 $0 -$10 -$20 -$30 Unde rlying Asse t Price $56.00 $55.00 $54.00 $53.00 $52.00 $51.00 $50.00 $49.00 $48.00 $47.00 $46.00 $45.00 $44.00 $43.00 $42.00 $41.00 $40.00 $39.00 $38.00 $37.00 $36.00 $35.00 $34.00 $33.00 $32.00 $31.00 $30.00 $29.00 $28.00 $27.00 $26.00 $25.00 $24.00 $23.00 $22.00 $21.00 $20.00 $19.00 $18.00 $17.00 $16.00 $15.00 $14.00 $13.00 $12.00 $11.00 $10.00 $9.00 $8.00 $7.00 -$76.00 -$75.00 -$74.00 -$73.00 -$72.00 -$71.00 -$70.00 -$69.00 -$68.00 -$67.00 -$66.00 -$65.00 -$64.00 -$63.00 -$62.00 -$61.00 -$60.00 -$59.00 -$58.00 -$57.00 -$56.00 -$55.00 -$54.00 -$53.00 -$52.00 -$51.00 -$50.00 -$49.00 -$48.00 -$47.00 -$46.00 -$45.00 -$44.00 -$43.00 -$42.00 -$41.00 -$40.00 -$39.00 -$38.00 -$37.00 -$36.00 -$35.00 -$34.00 -$33.00 -$32.00 -$31.00 -$30.00 -$29.00 -$28.00 -$27.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 $6.00 $5.00 $4.00 $3.00 $2.00 $1.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 -$26.00 -$25.00 -$24.00 -$23.00 -$22.00 -$21.00 -$20.00 -$19.00 -$18.00 -$17.00 -$16.00 -$15.00 -$14.00 -$13.00 -$12.00 -$11.00 -$10.00 -$9.00 -$8.00 -$7.00 -$6.00 -$5.00 -$4.00 -$3.00 -$2.00 -$1.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1.00 $2.00 $3.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$19.00 -$18.00 -$17.00 -$16.00 -$15.00 -$14.00 -$13.00 -$12.00 -$11.00 -$10.00 -$9.00 -$8.00 -$7.00 -$6.00 -$5.00 -$4.00 -$3.00 -$2.00 -$1.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1.00 $2.00 $3.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00 $11.00 $12.00 $13.00 $14.00 $15.00 $16.00 $17.00 $18.00 $19.00 $20.00 $21.00 $22.00 $23.00 $24.00 $25.00 $26.00 $27.00 $28.00 $29.00 $30.00 $31.00 $32.00 $33.00 $34.00 $35.00 $36.00 $37.00 $38.00 $39.00 $40.00 $41.00 $42.00 $43.00 $44.00 $45.00 $46.00 $47.00 $48.00 $49.00 $50.00 $51.00 $52.00 $53.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00 $11.00 $12.00 $13.00 $14.00 $15.00 $16.00 $17.00 $18.00 $19.00 $20.00 $21.00 $22.00 $23.00 $24.00 $25.00 $26.00 $27.00 $28.00 $29.00 $30.00 $31.00 $32.00 $33.00 $34.00 $35.00 $36.00 $37.00 $38.00 $39.00 $40.00 $41.00 $42.00 $43.00 $44.00 $45.00 $46.00 $47.00 $48.00 $49.00 $50.00 $51.00 $52.00 $53.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $54.00 $55.00 $56.00 $57.00 $58.00 $59.00 $60.00 $54.00 $55.00 $56.00 $57.00 $58.00 $59.00 $60.00 Total Portfolio Payof tfolio Payof Unde rlying Asse t Price Derivatives Project September 2017 Part A Payoff for P1 (K1 ) Since the portfolio is short in option P1 (K1 ), it follows that the payoff is: P1 (K1 ) Payoff = max (0, K1 S) (1) where S denotes the underlying asset price. Payoff for C2 (K2 ) Since the portfolio is long in option C2 (K2 ), it follows that the payoff is: C2 (K2 ) Payoff = max (0, S K2 ) (2) where K1 S0 (1 + i)T , it follows that the arbitrageur would make a risk-free trading profit equal to Forward price S0 (1 + i)T . Arbitrageurs would increase the demand for short positions of such a forward contract, thereby exerting a downward pressure on the forward price. It can be shown that when the forward price is less than S0 (1 + i)T , the action of arbitrageurs would exert an upward pressure on the forward price. Equilibrium is attained when Equation 8 is satisfied. Why Futures may Have Less Risk The counter-party to every futures trade is the clearinghouse. In virtually all cases, clearinghouses have a high creditworthiness. This makes the default risk inherent in futures contracts to be negligible. Each party to a futures trade is compelled to post a margin, which acts as collateral. The position of a trader is marked-to-market daily, with the profit/loss being posted to the margin account. If the margin account drops below the maintenance margin, the party receives a margin call, which requires him/her to top-up the margin account. Failure to top-up the margin account results in the futures contract being closed out. In summary, it is the mechanism of running a margin account and marking to market on a daily basis that significantly reduces the risk involved in futures. Unlike forwards, which are private transactions, futures markets tend to be regulated. The regulator would seek to protect the interests of the traders in the futures contracts. 3 100 S 100 50 0 -50 -100 -150 P1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 -100 -99 -98 -97 -96 Total -95 -94 -93 -92 -91 -90 -89 -88 -87 -86 -85 -84 -83 Total -82 -81 -80 -79 -78 -77 -76 -75 -74 -73 -72 -71 -70 -69 -68 -67 -66 -65 -64 -63 -62 -61 -60 -59 -58 -57 -56 -55 -54 120 C2 Total 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -100 -99 -98 -97 -96 -95 -94 -93 -92 -91 -90 -89 -88 -87 -86 -85 -84 -83 -82 -81 -80 -79 -78 -77 -76 -75 -74 -73 -72 -71 -70 -69 -68 -67 -66 -65 -64 -63 -62 -61 -60 -59 -58 -57 -56 -55 -54 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 -53 -52 -51 -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -53 -52 -51 -50 -49 -48 -47 -46 -45 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 -3 -2 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 197 198 199 200 0 0 0 0 77 78 79 80 77 78 79 80 Share Price Range S K2 P1 -max(0,K1-S)= K1-S -max(0,K1-S)= 0 -max(0,K1-S)= 0 C2 Total max(0,S-K2)=0 S-K_1 max(0,S-K2)=0 max(0,S-K2)=S-K2 S-K2 0 This sheet demonstrates Part B of the solution with the aid of a numerical example Inputs K1 K3 - K2 = K2 - K1 Payoff Table $ $ 100.00 20.00 ... Strikes equally spaced apart. Strike Values K1 K2 K3 $ $ $ 100.00 120.00 140.00 Notes .... Ideally, set input in cell C6 in a range between 5 to 40 for a better plot, given that K1 is set at a 100. ... The plot range for this illustration is where the share price is between 0 to 200 Share Price $0.00 $1.00 $2.00 $3.00 $4.00 $5.00 $6.00 $7.00 $8.00 $9.00 $10.00 $11.00 $12.00 $13.00 $14.00 $15.00 $16.00 $17.00 $18.00 $19.00 $20.00 $21.00 $22.00 $23.00 $24.00 $25.00 $26.00 $27.00 $28.00 $29.00 $30.00 $31.00 $32.00 $33.00 $34.00 $35.00 $36.00 $37.00 $38.00 $39.00 $40.00 $41.00 $42.00 $43.00 $44.00 $45.00 $46.00 $47.00 $48.00 $49.00 $50.00 $51.00 $52.00 $53.00 $54.00 $55.00 $56.00 $57.00 $58.00 $59.00 $60.00 $61.00 $62.00 $63.00 $64.00 $65.00 $66.00 $67.00 $68.00 $69.00 $70.00 $71.00 $72.00 $73.00 $74.00 $75.00 $76.00 $77.00 $78.00 $79.00 $80.00 $81.00 $82.00 $83.00 $84.00 $85.00 $86.00 $87.00 $88.00 $89.00 $90.00 $91.00 $92.00 $93.00 $94.00 $95.00 $96.00 $97.00 $98.00 $99.00 $100.00 $101.00 $102.00 $103.00 $104.00 $105.00 $106.00 $107.00 $108.00 $109.00 $110.00 $111.00 $112.00 $113.00 $114.00 $115.00 $116.00 $117.00 $118.00 $119.00 $120.00 $121.00 $122.00 $123.00 $124.00 $125.00 $126.00 $127.00 $128.00 $129.00 $130.00 $131.00 $132.00 $133.00 $134.00 $135.00 $136.00 $137.00 $138.00 $139.00 $140.00 $141.00 $142.00 $143.00 $144.00 $145.00 $146.00 $147.00 $148.00 $149.00 $150.00 $151.00 $152.00 $153.00 $154.00 $155.00 $156.00 $157.00 $158.00 $159.00 $160.00 $161.00 $162.00 $163.00 $164.00 $165.00 $166.00 $167.00 $168.00 $169.00 $170.00 $171.00 $172.00 $173.00 $174.00 $175.00 $176.00 $177.00 $178.00 $179.00 $180.00 $181.00 $182.00 $183.00 $184.00 $185.00 $186.00 $187.00 $188.00 $189.00 $190.00 $191.00 $192.00 $193.00 $194.00 $195.00 $196.00 $197.00 $198.00 $199.00 $200.00 Plot of Portfolio Payoff C3(K3) $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 Total Portfolio Payoff -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 Total Portfolio Payof $70 $60 Total Portfolio Payof $50 $40 Payoff P1(K1) $100.00 $99.00 $98.00 $97.00 $96.00 $95.00 $94.00 $93.00 $92.00 $91.00 $90.00 $89.00 $88.00 $87.00 $86.00 $85.00 $84.00 $83.00 $82.00 $81.00 $80.00 $79.00 $78.00 $77.00 $76.00 $75.00 $74.00 $73.00 $72.00 $71.00 $70.00 $69.00 $68.00 $67.00 $66.00 $65.00 $64.00 $63.00 $62.00 $61.00 $60.00 $59.00 $58.00 $57.00 Payoff P2(K2) -$120.00 -$119.00 -$118.00 -$117.00 -$116.00 -$115.00 -$114.00 -$113.00 -$112.00 -$111.00 -$110.00 -$109.00 -$108.00 -$107.00 -$106.00 -$105.00 -$104.00 -$103.00 -$102.00 -$101.00 -$100.00 -$99.00 -$98.00 -$97.00 -$96.00 -$95.00 -$94.00 -$93.00 -$92.00 -$91.00 -$90.00 -$89.00 -$88.00 -$87.00 -$86.00 -$85.00 -$84.00 -$83.00 -$82.00 -$81.00 -$80.00 -$79.00 -$78.00 -$77.00 $30 $20 $10 $0 -$10 -$20 -$30 Unde rlying Asse t Price $56.00 $55.00 $54.00 $53.00 $52.00 $51.00 $50.00 $49.00 $48.00 $47.00 $46.00 $45.00 $44.00 $43.00 $42.00 $41.00 $40.00 $39.00 $38.00 $37.00 $36.00 $35.00 $34.00 $33.00 $32.00 $31.00 $30.00 $29.00 $28.00 $27.00 $26.00 $25.00 $24.00 $23.00 $22.00 $21.00 $20.00 $19.00 $18.00 $17.00 $16.00 $15.00 $14.00 $13.00 $12.00 $11.00 $10.00 $9.00 $8.00 $7.00 -$76.00 -$75.00 -$74.00 -$73.00 -$72.00 -$71.00 -$70.00 -$69.00 -$68.00 -$67.00 -$66.00 -$65.00 -$64.00 -$63.00 -$62.00 -$61.00 -$60.00 -$59.00 -$58.00 -$57.00 -$56.00 -$55.00 -$54.00 -$53.00 -$52.00 -$51.00 -$50.00 -$49.00 -$48.00 -$47.00 -$46.00 -$45.00 -$44.00 -$43.00 -$42.00 -$41.00 -$40.00 -$39.00 -$38.00 -$37.00 -$36.00 -$35.00 -$34.00 -$33.00 -$32.00 -$31.00 -$30.00 -$29.00 -$28.00 -$27.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 $6.00 $5.00 $4.00 $3.00 $2.00 $1.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 -$26.00 -$25.00 -$24.00 -$23.00 -$22.00 -$21.00 -$20.00 -$19.00 -$18.00 -$17.00 -$16.00 -$15.00 -$14.00 -$13.00 -$12.00 -$11.00 -$10.00 -$9.00 -$8.00 -$7.00 -$6.00 -$5.00 -$4.00 -$3.00 -$2.00 -$1.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1.00 $2.00 $3.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$20.00 -$19.00 -$18.00 -$17.00 -$16.00 -$15.00 -$14.00 -$13.00 -$12.00 -$11.00 -$10.00 -$9.00 -$8.00 -$7.00 -$6.00 -$5.00 -$4.00 -$3.00 -$2.00 -$1.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $1.00 $2.00 $3.00 $0.00 $0.00