. Using the Black-Scholes pricing function in Excel, compute an option value for each strike price and maturity date in case Exhibit 2. For simplicity, assume zero dividend yield. Also, use Louise Itos volatility estimates, provided in case Exhibit 1.

... ... ... Exhibit 2 ITO'S DILEMMA Option Premium and Market Data for February 20, 2001 Call Premiums Put Premiums Mar Apr July Mar Apr July Duke Energy 42.27 40 4.30 5.30 0.75 1.30 2.25 42.27 42.5 2.70 3.90 4.80 2.40 42.27 45 1.25 2.40 3.30 IBM 108.9 100 12.00 14.10 18.70 2.20 4.30 7.00 108.9 110 4.40 8.10 11.40 5.30 8.10 10.50 108.9 120 1.10 3.60 7.50 12.20 13.90 15.60 Microsoft 55.188 50 6.50 8.13 10.00 1.19 2.50 4.00 55.188 55 3.00 4.50 6.88 2.69 4.13 6.00 55.188 60 0.94 2.38 4.50 5.38 6.75 8.13 ... T-bill rates 4.92% 4.85% 4.85% 4.91% Expiration date 17-Mar 21-Apr 21-Jul Days to expiration 25 60 151 36,942 36,942 36,942 4.92% 4.85% 4.91% 17-Mar 21-Apr 21-Jul 25 60 151 ITO'S DILEMMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft Returns (In) Duke Energ IBM Microsoft Prices Week No Date Duke Energ IBM Close Close 36,731 30.84 111.419 1 31-Jul-00 33.16 115.47 2 07-Aug-00 33.58 120.34 3 14-Aug-00 34.32 120.15 4 21-Aug-00 34.75 128.69 5 28-Aug-00 36.89 133.30 6 04-Sep-00 39.64 129.19 7 11-Sep-00 40.10 124.70 8 18-Sep-00 37.44 123.58 9 25-Sep-00 42.32 112.35 10 02-Oct-00 40.37 115.72 11 09-Oct-00 42.00 108.80 12 16-Oct-00 42.59 94.52 13 23-Oct-00 40.95 93.46 14 30-Oct-00 41.97 99.88 15 06-Nov-00 43.17 92.89 16 13-Nov-00 43.83 101.82 17 20-Nov-00 42.71 99.82 18 27-Nov-00 43.33 95.52 19 04-Dec-00 42.59 96.89 20 11-Dec-00 41.06 87.71 21 18-Dec-00 41.96 88.90 22 25-Dec-00 36.25 93.89 23 01-Jan-01 41.10 84.72 24 08-Jan-01 34.83 93.71 25 15-Jan-01 36.16 111.12 26 22-Jan-01 38.24 114.06 27 29-Jan-01 37.33 110.14 28 05-Feb-01 41.02 112.00 29 12-Feb-01 41.16 115.00 30 19-Feb-01 42.27 108.90 Microsoft Close 69.688 69.12 72.44 71.00 70.62 70.19 69.31 64.19 63.25 60.31 55.56 53.75 65.19 67.69 68.25 67.38 69.06 69.94 56.62 54.44 49.19 46.44 49.12 43.38 53.50 61.00 64.00 60.81 59.12 57.31 55.19 7.27% 1.25% 2.18% 1.25% 5.96% 7.20% 1.14% -6.86% 12.25% -4.72% 3.97% 1.39% -3.91% 2.45% 2.83% 1.51% -2.58% 1.44% -1.73% -3.64% 2.17% -14.63% 12.54% -16.55% 3.76% 5.59% -2.42% 9.44% 0.34% 2.66% 3.57% -0.81% 4.13% 4.68% -0.16% -2.00% 6.87% -0.53% 3.52% -0.62% -3.14% -1.25% -3.54% -7.68% -0.90% -1.47% -9.52% -4.76% 2.95% -8.20% -6.17% -3.32% -14.07% 19.29% -1.13% 3.76% 6.65% 0.83% -7.25% -1.29% 9.18% 2.47% -1.98% 1.26% -4.41% -21.12% 1.43% -3.94% -9.95% -10.14% 1.34% -5.75% 5.47% 5.63% -10.29% -12.45% 10.09% 20.98% 17.05% 13.12% 2.61% 4.80% -3.49% -5.11% 1.67% -2.81% 2.64% -3.11% -5.45% -3.78% Weekly Sigma of Returns 6.34% Annualized standard deviation of return$5.75% 6.69% 48.24% 8.26% 59.56% ... ... ... Exhibit 2 ITO'S DILEMMA Option Premium and Market Data for February 20, 2001 Call Premiums Put Premiums Mar Apr July Mar Apr July Duke Energy 42.27 40 4.30 5.30 0.75 1.30 2.25 42.27 42.5 2.70 3.90 4.80 2.40 42.27 45 1.25 2.40 3.30 IBM 108.9 100 12.00 14.10 18.70 2.20 4.30 7.00 108.9 110 4.40 8.10 11.40 5.30 8.10 10.50 108.9 120 1.10 3.60 7.50 12.20 13.90 15.60 Microsoft 55.188 50 6.50 8.13 10.00 1.19 2.50 4.00 55.188 55 3.00 4.50 6.88 2.69 4.13 6.00 55.188 60 0.94 2.38 4.50 5.38 6.75 8.13 ... T-bill rates 4.92% 4.85% 4.85% 4.91% Expiration date 17-Mar 21-Apr 21-Jul Days to expiration 25 60 151 36,942 36,942 36,942 4.92% 4.85% 4.91% 17-Mar 21-Apr 21-Jul 25 60 151 ITO'S DILEMMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft Returns (In) Duke Energ IBM Microsoft Prices Week No Date Duke Energ IBM Close Close 36,731 30.84 111.419 1 31-Jul-00 33.16 115.47 2 07-Aug-00 33.58 120.34 3 14-Aug-00 34.32 120.15 4 21-Aug-00 34.75 128.69 5 28-Aug-00 36.89 133.30 6 04-Sep-00 39.64 129.19 7 11-Sep-00 40.10 124.70 8 18-Sep-00 37.44 123.58 9 25-Sep-00 42.32 112.35 10 02-Oct-00 40.37 115.72 11 09-Oct-00 42.00 108.80 12 16-Oct-00 42.59 94.52 13 23-Oct-00 40.95 93.46 14 30-Oct-00 41.97 99.88 15 06-Nov-00 43.17 92.89 16 13-Nov-00 43.83 101.82 17 20-Nov-00 42.71 99.82 18 27-Nov-00 43.33 95.52 19 04-Dec-00 42.59 96.89 20 11-Dec-00 41.06 87.71 21 18-Dec-00 41.96 88.90 22 25-Dec-00 36.25 93.89 23 01-Jan-01 41.10 84.72 24 08-Jan-01 34.83 93.71 25 15-Jan-01 36.16 111.12 26 22-Jan-01 38.24 114.06 27 29-Jan-01 37.33 110.14 28 05-Feb-01 41.02 112.00 29 12-Feb-01 41.16 115.00 30 19-Feb-01 42.27 108.90 Microsoft Close 69.688 69.12 72.44 71.00 70.62 70.19 69.31 64.19 63.25 60.31 55.56 53.75 65.19 67.69 68.25 67.38 69.06 69.94 56.62 54.44 49.19 46.44 49.12 43.38 53.50 61.00 64.00 60.81 59.12 57.31 55.19 7.27% 1.25% 2.18% 1.25% 5.96% 7.20% 1.14% -6.86% 12.25% -4.72% 3.97% 1.39% -3.91% 2.45% 2.83% 1.51% -2.58% 1.44% -1.73% -3.64% 2.17% -14.63% 12.54% -16.55% 3.76% 5.59% -2.42% 9.44% 0.34% 2.66% 3.57% -0.81% 4.13% 4.68% -0.16% -2.00% 6.87% -0.53% 3.52% -0.62% -3.14% -1.25% -3.54% -7.68% -0.90% -1.47% -9.52% -4.76% 2.95% -8.20% -6.17% -3.32% -14.07% 19.29% -1.13% 3.76% 6.65% 0.83% -7.25% -1.29% 9.18% 2.47% -1.98% 1.26% -4.41% -21.12% 1.43% -3.94% -9.95% -10.14% 1.34% -5.75% 5.47% 5.63% -10.29% -12.45% 10.09% 20.98% 17.05% 13.12% 2.61% 4.80% -3.49% -5.11% 1.67% -2.81% 2.64% -3.11% -5.45% -3.78% Weekly Sigma of Returns 6.34% Annualized standard deviation of return$5.75% 6.69% 48.24% 8.26% 59.56%