Question 1.

(i) Using the information from the Friday, October 26, 1996 Wall Street Journal, calculate the implied volatility from the S&P 100 index (put only). In particular, calculate for all strike/exercise prices between 660 and 680 for options expiring in December and January only. Note that by design index options expire on the 3rd Friday of each month so calculate the time to maturity accordingly (assume 365 day year). In addition, use the risk-free rate (T-Bills) closest to expiration date of the option. Remember that the RF rate is quoted in annualized terms.

Graph the implied volatility against the strike price on a separate graph for December and January.

Is the volatility constant?

To solve for the implied volatility you may use trial and error by equating the theoretical price from B-S (which you must compute) to the actual market (closing price) by trial and error, i.e. varying s, but I recommend using either the Solver or Goal Seek function in Excel.

(ii) Use the above data to estimate delta. Create graph in excel.

(iii) Use the above data to estimate gamma. Create graph in excel.

Needs to be done in Excel With Formulas Please

THE WALL STREET JOURNAL FRIDAY, OCTOBER 25. 1996 C141 INDEX OPTIONS TRADING 5750 315p dwojenne gange PROGRAREKASS 10 ************************#Issiussss Closing Price "!++++++++++++++++++++++ RANGES FOR UNDERLYING INDEXES Thursday, October 24, 1996 Net Frum High Low Cose Chr. Dec. 21 % Che. S&P 100 (OBB) $85.23 678.48 685.01 + 1.01 + 99.09 + 16.9 S&P 500 A.M.(SEX). 707.31 700.98 707.17 + 0.70 + 91.34 + 2.8 S&P Banks (BDO-22.64 418.8 122,00 + 0.73 + 92.10 + 27.9 CB-Tech (moh. 183.62 178.85 183.36 + 2.81 + 26.83 +. 17.1 CB-Mexico (MEX). 82.59 40.59 82.55 + 0.32 + 10.81 + 15.1 CB-Lps Mex (VEX. 8.26 8.06 8.25 + 0.04 + 209 + 15.2 Nasdaq 100 (NDR)._ 750.59 732.63 749.70 +13.06 + 173.47 + 30.1 Russell 2000 (RUT). 312.93 341.31 342.93 + 0.11 + 26.96 + 8.5 Lps S&P 100 (OE). 68.52 67.85 68.50 + 0.10 + 9.91 + 16.9 Lps S&P 500 (SPX). 70.3 70.10 70.73 + 0.07 + 9.14 + 14.8 SLP Midcap (MID).. 243.74 241.95 243.60 + 0.78 + 28.75 + 11.8 Major Mkt om 526.32 619.46 625.49 0.34 + 89.89 + 16.8 Leaps MMkt (XLT). 62.63 61.95 62.55 0.03 +. 8.99 + 16.8 Hong Kong (HKOI... 252.86 + 1.00 + 49.95 + 246 Leaps HK (HKL). 25.29 + 0.10 + 5.00 + 206 IW internet (DX)_... 246.34 238.53 246.01 + 4.80 + 12.81 + AM-Mexico (07... 92.01 89.53 91.02 +0.74 + 8.2 + LE Institut A.M.OT). 755.21 748.16 754.95 -0.26 +178.23 + 2 Japan JPN) 214.21 0.47 + 12.37 + MS Cyclical (CYC)... 374.69 371.19 373.96 0.73 + 33.74 + MS Consum (CMR326.33 322.95 326.07 -0.26 + (1.32 + 10 MS HA Tech (MSH) .. 352.47 346.97 351.57 +2.44 + 35.80 + 1 Pharm DRG). 356.00 352.10 356.79 + 0.01 + 59.84 + 21 Blotech (BTR) 133,39 131.41 133.31 + 0.30 - 0.46 0.2 Comp Tech exch)... 302.02 294.25 301.50 + 5.31 + 7288 + 329 NYSE (NYA). 376.72 373.24 375.91 0.31 + 46.0 + 14.1 Gold/Silver (XAU)... 119.81 117.49 119.25 + 0.65 - 1.17 - 1.0 PTC OC. 533.97 572.36 533.11 + 8.17 + 108.41 + 25.5 Utility cum 251.05 248.92 251.02 -0.04 - 25.58 - 9.6 Yalye Line (VLE..... 545.58 642.03 645.57 + 3.46 + 75.67 + 13.3 Bank DKI 500.26 495.64 500.20 + 0.87 + 106.36 + 27.0 Setnicond (SOX)... 193.82 187.34 193.48 + 1.38 - 7.18 - 3.6 Top 100 TPX)..... G46.92 640.82 646.86 - 0.44 + 93.84 + 17.0 PSE Tech (PS). 21.88 218.07 721.74 +2.00 + 19.97 + 9.9 2500 Feb 550 Gos $4 P 100 INDEX(OEX) NON 360p + W Nov 5450 100 NOV 70p J Nov The - A+ Dec 9900 Nov 9954 Nov Sp 110 772 NOV 6000 211 W 2.09 DES 600D 244 a 3.955 Nov 403e W 2781 Nov 610p 14 W 2718 Dec 6100 5 905 Nov ti W 4000 Dec 415p 149 Nov 6200 124 12.AT Dec 420p 7.16 Nov 6250 7,218 Dec. 6730 - 2.129 Jen 1250 16 10 Now 30 2216 W JW W Nov $700 1,100 * 4.736 Otc 4.221 JAR 420p 316 1351 Feb 200 9 12 NOV ESP 165 12941 Dec 4350 7 1,706 4337 12 20 NOV 6406 2116 NOV MOD Dec 640D 26 NOV 65C 105 V 2,025 Nov uso 225$ T4 20.585 Dec Sp 4,977 Nov 4900 6% 2,219 NOV 650 2.501 19 121 Dec 650D 415 + 4276 Jan 562 65CD 46 6555 1468 NOY 6550 2.433 118.7 Det 3,137 Nov 600C 0 7.757 NOV 8600 2.77 2 2670 Dec 6604 10 1441 Dec 17 16 6,636 Jan 650D 202 616 Ft 0600 204 Hov 102 6,7 Nov Map , Dec 0:50 22 11,242 jan 110V NOV 670e 4 15 SV 9.047 NOV 6700 4,007 7% 24 14,091 Das 67 1 J 1.20! 670D 22 11 2 3,961 Nov 6750 1,702 1215 SVA 6.077 Nov 4750 10,409 96 312624 Doc 4752 27 154 + 114 JAT 6750 216 + 725 NOV 680C 5,716 04-4 11.573 NOV tap 19.240 1744 + 4V 16,210 4800 205 177 -4 2A77 Dos 600p 199 17 + 3 1.37 Jan 400C 30 21% -1% 586 Jan 480p 677 2014 + 4 Fee 080p 109 714 - OP NOV 4656 11.43 7 - ** 14658 MOM Asp 6.076 144 + 47 11,414 Dec 655C 100 18% - 2503 Sp 26 204 + sy 1,150 Nov 670C 10,357 $ 2 V.ATT Nov 480p 1.243 174 + 4% 4441 Dec Wc Ich 16 1.25 Dec 6700 17 21% + 1% 576 Jan 490 209 17 34 368 Jan * 5107 Feb POC 100 22 22 Feb 4900 103 77 2W OCC 15 10 700C 4,543 2x 14 Nov 700D 22 2495 + 5 Des DOC 4 2.0 Det 7000 TH 7005 ? 1745 Feb 700P $ 30% 15 Nov 705 C 2416 1778 1 2,002 Nov 710C 2.702 4 8.112 7100 100 6 19 1.878 7100 1341 31 22 NOV 737 the ma Dee 7156 242 3% 14 899 Nov 720e 865 VA 2.34 Dec 720C 210 VA Dec 720p 10 Nev 7250 1,346 ah 1.330 Nov 7306 WA DES 7 105 3.589 NOY 713 65 ha $30 Des + 130 Call Vol, 55,144 Open In! 164,288 Put Vol. 65,010 Open Int, 904450 Mp 2700 Jan Dec 600D EHL 6950 TREASURY BILLS Ders to Atk Maturity Metald Asked Cho. Yld. od 3T 64.73 4.71 +0.BP 4.8 Nov 07 v 0476 NOV 14 JT 477 +0.01 4.ES Nov 21 96 77 77 +0.01 4.25 Nov 29 35 CM 480 +0.64 UN Dec 41 4X CH +0.01 4.98 Dec 127 44.90 446 +0.01 . Dec 19 55 49 41 +0.R 491 Dec 26%40 41 +0.01 Jan 29 M 4 +0.09 4.95 Jan 0 97 76 49 492 5.04 Jan 1897 4.99 4.9 40.5.10 Jan 23 0 4.72 1 + 0.01 $.11 Jan 3097 77 5.92 5.00 0.00 114 Jan 0 n 5.0 LN + .tz Feb 05 71 104 5.02 5.0 +2.03 5.14 Feb 1397 111 5.B 4.90 +0.25.13 Feb 2097 118 5.01 4.99 +0.07 5.14 Feb 27 128 5.45 +0.01 5.1! Mar 06 97 5.0 5.04 40.02 5.21 Mar 13 917 9.065.04 +0.01 5.21 Mar 29 146 5.4 5.0 5121 Mar 27 97 153 4.97 4.95 $.13 Abr 97 160 5.0 5.06 -0.02 $35 Apr 109 767 5.11 5.00 5.29 Apr 1797 174 5.12 5.10 5. Apr 24 9 181 S.12 5.11 +0.01 $. May 01 Y 146 5.15 5.11 +0.01 534 Mayer 1 5.00 5.tz 0.07 53 Mav 216 5.15 5.13 +0.01 5.34 Jun 26 9 24 5.11 5.15 +0.01 Jul 24 07 2725.2 5.20 +0.025.4 Aug 21 7 300 5.74 5.22 +0.01 5.0 Sed 1997 5.2 5.21 5.48 Del 1697 356 5.26 5.25 +0.01 5.34 Feb TIS ,4 2.670 740 5.37 THE WALL STREET JOURNAL FRIDAY, OCTOBER 25. 1996 C141 INDEX OPTIONS TRADING 5750 315p dwojenne gange PROGRAREKASS 10 ************************#Issiussss Closing Price "!++++++++++++++++++++++ RANGES FOR UNDERLYING INDEXES Thursday, October 24, 1996 Net Frum High Low Cose Chr. Dec. 21 % Che. S&P 100 (OBB) $85.23 678.48 685.01 + 1.01 + 99.09 + 16.9 S&P 500 A.M.(SEX). 707.31 700.98 707.17 + 0.70 + 91.34 + 2.8 S&P Banks (BDO-22.64 418.8 122,00 + 0.73 + 92.10 + 27.9 CB-Tech (moh. 183.62 178.85 183.36 + 2.81 + 26.83 +. 17.1 CB-Mexico (MEX). 82.59 40.59 82.55 + 0.32 + 10.81 + 15.1 CB-Lps Mex (VEX. 8.26 8.06 8.25 + 0.04 + 209 + 15.2 Nasdaq 100 (NDR)._ 750.59 732.63 749.70 +13.06 + 173.47 + 30.1 Russell 2000 (RUT). 312.93 341.31 342.93 + 0.11 + 26.96 + 8.5 Lps S&P 100 (OE). 68.52 67.85 68.50 + 0.10 + 9.91 + 16.9 Lps S&P 500 (SPX). 70.3 70.10 70.73 + 0.07 + 9.14 + 14.8 SLP Midcap (MID).. 243.74 241.95 243.60 + 0.78 + 28.75 + 11.8 Major Mkt om 526.32 619.46 625.49 0.34 + 89.89 + 16.8 Leaps MMkt (XLT). 62.63 61.95 62.55 0.03 +. 8.99 + 16.8 Hong Kong (HKOI... 252.86 + 1.00 + 49.95 + 246 Leaps HK (HKL). 25.29 + 0.10 + 5.00 + 206 IW internet (DX)_... 246.34 238.53 246.01 + 4.80 + 12.81 + AM-Mexico (07... 92.01 89.53 91.02 +0.74 + 8.2 + LE Institut A.M.OT). 755.21 748.16 754.95 -0.26 +178.23 + 2 Japan JPN) 214.21 0.47 + 12.37 + MS Cyclical (CYC)... 374.69 371.19 373.96 0.73 + 33.74 + MS Consum (CMR326.33 322.95 326.07 -0.26 + (1.32 + 10 MS HA Tech (MSH) .. 352.47 346.97 351.57 +2.44 + 35.80 + 1 Pharm DRG). 356.00 352.10 356.79 + 0.01 + 59.84 + 21 Blotech (BTR) 133,39 131.41 133.31 + 0.30 - 0.46 0.2 Comp Tech exch)... 302.02 294.25 301.50 + 5.31 + 7288 + 329 NYSE (NYA). 376.72 373.24 375.91 0.31 + 46.0 + 14.1 Gold/Silver (XAU)... 119.81 117.49 119.25 + 0.65 - 1.17 - 1.0 PTC OC. 533.97 572.36 533.11 + 8.17 + 108.41 + 25.5 Utility cum 251.05 248.92 251.02 -0.04 - 25.58 - 9.6 Yalye Line (VLE..... 545.58 642.03 645.57 + 3.46 + 75.67 + 13.3 Bank DKI 500.26 495.64 500.20 + 0.87 + 106.36 + 27.0 Setnicond (SOX)... 193.82 187.34 193.48 + 1.38 - 7.18 - 3.6 Top 100 TPX)..... G46.92 640.82 646.86 - 0.44 + 93.84 + 17.0 PSE Tech (PS). 21.88 218.07 721.74 +2.00 + 19.97 + 9.9 2500 Feb 550 Gos $4 P 100 INDEX(OEX) NON 360p + W Nov 5450 100 NOV 70p J Nov The - A+ Dec 9900 Nov 9954 Nov Sp 110 772 NOV 6000 211 W 2.09 DES 600D 244 a 3.955 Nov 403e W 2781 Nov 610p 14 W 2718 Dec 6100 5 905 Nov ti W 4000 Dec 415p 149 Nov 6200 124 12.AT Dec 420p 7.16 Nov 6250 7,218 Dec. 6730 - 2.129 Jen 1250 16 10 Now 30 2216 W JW W Nov $700 1,100 * 4.736 Otc 4.221 JAR 420p 316 1351 Feb 200 9 12 NOV ESP 165 12941 Dec 4350 7 1,706 4337 12 20 NOV 6406 2116 NOV MOD Dec 640D 26 NOV 65C 105 V 2,025 Nov uso 225$ T4 20.585 Dec Sp 4,977 Nov 4900 6% 2,219 NOV 650 2.501 19 121 Dec 650D 415 + 4276 Jan 562 65CD 46 6555 1468 NOY 6550 2.433 118.7 Det 3,137 Nov 600C 0 7.757 NOV 8600 2.77 2 2670 Dec 6604 10 1441 Dec 17 16 6,636 Jan 650D 202 616 Ft 0600 204 Hov 102 6,7 Nov Map , Dec 0:50 22 11,242 jan 110V NOV 670e 4 15 SV 9.047 NOV 6700 4,007 7% 24 14,091 Das 67 1 J 1.20! 670D 22 11 2 3,961 Nov 6750 1,702 1215 SVA 6.077 Nov 4750 10,409 96 312624 Doc 4752 27 154 + 114 JAT 6750 216 + 725 NOV 680C 5,716 04-4 11.573 NOV tap 19.240 1744 + 4V 16,210 4800 205 177 -4 2A77 Dos 600p 199 17 + 3 1.37 Jan 400C 30 21% -1% 586 Jan 480p 677 2014 + 4 Fee 080p 109 714 - OP NOV 4656 11.43 7 - ** 14658 MOM Asp 6.076 144 + 47 11,414 Dec 655C 100 18% - 2503 Sp 26 204 + sy 1,150 Nov 670C 10,357 $ 2 V.ATT Nov 480p 1.243 174 + 4% 4441 Dec Wc Ich 16 1.25 Dec 6700 17 21% + 1% 576 Jan 490 209 17 34 368 Jan * 5107 Feb POC 100 22 22 Feb 4900 103 77 2W OCC 15 10 700C 4,543 2x 14 Nov 700D 22 2495 + 5 Des DOC 4 2.0 Det 7000 TH 7005 ? 1745 Feb 700P $ 30% 15 Nov 705 C 2416 1778 1 2,002 Nov 710C 2.702 4 8.112 7100 100 6 19 1.878 7100 1341 31 22 NOV 737 the ma Dee 7156 242 3% 14 899 Nov 720e 865 VA 2.34 Dec 720C 210 VA Dec 720p 10 Nev 7250 1,346 ah 1.330 Nov 7306 WA DES 7 105 3.589 NOY 713 65 ha $30 Des + 130 Call Vol, 55,144 Open In! 164,288 Put Vol. 65,010 Open Int, 904450 Mp 2700 Jan Dec 600D EHL 6950 TREASURY BILLS Ders to Atk Maturity Metald Asked Cho. Yld. od 3T 64.73 4.71 +0.BP 4.8 Nov 07 v 0476 NOV 14 JT 477 +0.01 4.ES Nov 21 96 77 77 +0.01 4.25 Nov 29 35 CM 480 +0.64 UN Dec 41 4X CH +0.01 4.98 Dec 127 44.90 446 +0.01 . Dec 19 55 49 41 +0.R 491 Dec 26%40 41 +0.01 Jan 29 M 4 +0.09 4.95 Jan 0 97 76 49 492 5.04 Jan 1897 4.99 4.9 40.5.10 Jan 23 0 4.72 1 + 0.01 $.11 Jan 3097 77 5.92 5.00 0.00 114 Jan 0 n 5.0 LN + .tz Feb 05 71 104 5.02 5.0 +2.03 5.14 Feb 1397 111 5.B 4.90 +0.25.13 Feb 2097 118 5.01 4.99 +0.07 5.14 Feb 27 128 5.45 +0.01 5.1! Mar 06 97 5.0 5.04 40.02 5.21 Mar 13 917 9.065.04 +0.01 5.21 Mar 29 146 5.4 5.0 5121 Mar 27 97 153 4.97 4.95 $.13 Abr 97 160 5.0 5.06 -0.02 $35 Apr 109 767 5.11 5.00 5.29 Apr 1797 174 5.12 5.10 5. Apr 24 9 181 S.12 5.11 +0.01 $. May 01 Y 146 5.15 5.11 +0.01 534 Mayer 1 5.00 5.tz 0.07 53 Mav 216 5.15 5.13 +0.01 5.34 Jun 26 9 24 5.11 5.15 +0.01 Jul 24 07 2725.2 5.20 +0.025.4 Aug 21 7 300 5.74 5.22 +0.01 5.0 Sed 1997 5.2 5.21 5.48 Del 1697 356 5.26 5.25 +0.01 5.34 Feb TIS ,4 2.670 740 5.37