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.

A B D E F H I J K 2 Exhibiti ITOS DILENIMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft Prioes Duke Energy IBM Close Close Date Returns (In) Duke Energy IBM Microsoft Close Microsoft 4 5 6 Wock No. ? 9 1 10 2 11 3 12 4 13 5 14 6 15 7 16 8 17 9 18 10 19 11 20 12 21 13 22 14 23 15 24 16 25 17 26 18 27 19 28 20 29 21 30 22 31 23 32 24 33 25 34 26 35 27 36 28 37 29 38 30 39 40 41 42 43 31-Jul-00 07-Aug-00 14-Aug-00 21-Aug-00 28-Aug-00 04-Sep-00 11-Sep-00 18-Sep-00 25-Sep-00 02-Oct-00 09-Oct-00 16-Oct-00 23-Oct-00 30-Oct-00 06-Nov-00 13-Nov-00 20-Nov-00 27-Nov-00 04-Dec-00 11-Dec-00 18-Dec-00 25-Dec-00 01-Jan-01 08-Jan-01 15-Jan-01 22-Jan-01 29-Jan-01 05-Feb-01 12-Feb-01 19-Feb-01 33.16 33.58 34.32 34.75 36.89 39.64 40.10 37.44 42.32 40.37 42.00 42.59 40.95 41.97 43.17 43.83 42.71 43.33 42.59 41.06 41.96 36.25 41.10 34.83 36.16 38.24 37.33 41.02 41.16 42.27 115.47 120.34 120.15 128.69 133.30 129.19 124.70 123.58 112.35 115.72 108.80 94.52 93.46 99.88 92.89 101.82 99.82 95.52 96.89 87.71 88.90 93.89 84.72 93.71 111.12 114.06 110.14 112.00 115.00 108.90 69.13 72.44 71.00 70.63 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 56.63 54.44 49.19 46.44 49.13 43.38 53.50 61.00 64.00 60.81 59.13 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% 4.13% -0.16% 6.87% 3.52% -3.14% -3.54% -0.90% -9.52% 2.95% -6.17% -14.07% -1.13% 6.65% -7.25% 9.18% -1.98% 4.41% 1.43% -9.95% 1.34% 5.47% -10.29% 10.09% 17.05% 2.61% -3.49% 1.67% 2.64% -5.45% -0.81% 4.68% -2.00% -0.53% -0.62% -1.25% -7.68% -1.47% 4.76% -8.20% -3.32% 19.29% 3.76% 0.83% -1.29% 2.47% 1.26% -21.12% -3.94% -10.14% -5.75% 5.63% -12.45% 20.98% 13.12% 4.80% -5.11% -2.81% -3.11% -3.78% Weekly Sigma of Retums Annualized standard deviation of retums 6.34% 45.75% 6.69% 48.24% 8.26% 59.56% A B B c D G J K 1 2 F Exhibit 2 ITO'S DILEMMA Option Premium and Market Data for February 20, 2001 Call Premiums Put Premiums Mar Apr Mar Apr July 3 July ... 1.30 2.25 40 42.5 45 2.70 5 6 7 8 9 10 11 12 13 4.30 3.90 2.40 0.75 2.40 5.30 4.80 3.30 ... 1.25 ... ... Duke Energy 42.27 42.27 42.27 IBM 108.90 108.90 108.90 Microsoft 55.19 55.19 55.19 100 110 120 12.00 4.40 1.10 14.10 8.10 3.60 18.70 11.40 7.50 2.20 5.30 12.20 4.30 8.10 13.90 7.00 10.50 15.60 14 15 16 17 18 50 55 60 6.50 3.00 0.94 8.13 4.50 2.38 10.00 6.88 4.50 1.19 2.69 5.38 2.50 4.13 6.75 4.00 6.00 8.13 19 20 T-bill rates Expiration date Days to expiration 4.92% 17-Mar 25 4.85% 21-Apr 60 4.91% 21-Jul 151 4.92% 4.85% 4.91% 17-Mar 21-Apr 21-Jul 25 60 151 21 22 23 A B D E F H I J K 2 Exhibiti ITOS DILENIMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft Prioes Duke Energy IBM Close Close Date Returns (In) Duke Energy IBM Microsoft Close Microsoft 4 5 6 Wock No. ? 9 1 10 2 11 3 12 4 13 5 14 6 15 7 16 8 17 9 18 10 19 11 20 12 21 13 22 14 23 15 24 16 25 17 26 18 27 19 28 20 29 21 30 22 31 23 32 24 33 25 34 26 35 27 36 28 37 29 38 30 39 40 41 42 43 31-Jul-00 07-Aug-00 14-Aug-00 21-Aug-00 28-Aug-00 04-Sep-00 11-Sep-00 18-Sep-00 25-Sep-00 02-Oct-00 09-Oct-00 16-Oct-00 23-Oct-00 30-Oct-00 06-Nov-00 13-Nov-00 20-Nov-00 27-Nov-00 04-Dec-00 11-Dec-00 18-Dec-00 25-Dec-00 01-Jan-01 08-Jan-01 15-Jan-01 22-Jan-01 29-Jan-01 05-Feb-01 12-Feb-01 19-Feb-01 33.16 33.58 34.32 34.75 36.89 39.64 40.10 37.44 42.32 40.37 42.00 42.59 40.95 41.97 43.17 43.83 42.71 43.33 42.59 41.06 41.96 36.25 41.10 34.83 36.16 38.24 37.33 41.02 41.16 42.27 115.47 120.34 120.15 128.69 133.30 129.19 124.70 123.58 112.35 115.72 108.80 94.52 93.46 99.88 92.89 101.82 99.82 95.52 96.89 87.71 88.90 93.89 84.72 93.71 111.12 114.06 110.14 112.00 115.00 108.90 69.13 72.44 71.00 70.63 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 56.63 54.44 49.19 46.44 49.13 43.38 53.50 61.00 64.00 60.81 59.13 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% 4.13% -0.16% 6.87% 3.52% -3.14% -3.54% -0.90% -9.52% 2.95% -6.17% -14.07% -1.13% 6.65% -7.25% 9.18% -1.98% 4.41% 1.43% -9.95% 1.34% 5.47% -10.29% 10.09% 17.05% 2.61% -3.49% 1.67% 2.64% -5.45% -0.81% 4.68% -2.00% -0.53% -0.62% -1.25% -7.68% -1.47% 4.76% -8.20% -3.32% 19.29% 3.76% 0.83% -1.29% 2.47% 1.26% -21.12% -3.94% -10.14% -5.75% 5.63% -12.45% 20.98% 13.12% 4.80% -5.11% -2.81% -3.11% -3.78% Weekly Sigma of Retums Annualized standard deviation of retums 6.34% 45.75% 6.69% 48.24% 8.26% 59.56% A B B c D G J K 1 2 F Exhibit 2 ITO'S DILEMMA Option Premium and Market Data for February 20, 2001 Call Premiums Put Premiums Mar Apr Mar Apr July 3 July ... 1.30 2.25 40 42.5 45 2.70 5 6 7 8 9 10 11 12 13 4.30 3.90 2.40 0.75 2.40 5.30 4.80 3.30 ... 1.25 ... ... Duke Energy 42.27 42.27 42.27 IBM 108.90 108.90 108.90 Microsoft 55.19 55.19 55.19 100 110 120 12.00 4.40 1.10 14.10 8.10 3.60 18.70 11.40 7.50 2.20 5.30 12.20 4.30 8.10 13.90 7.00 10.50 15.60 14 15 16 17 18 50 55 60 6.50 3.00 0.94 8.13 4.50 2.38 10.00 6.88 4.50 1.19 2.69 5.38 2.50 4.13 6.75 4.00 6.00 8.13 19 20 T-bill rates Expiration date Days to expiration 4.92% 17-Mar 25 4.85% 21-Apr 60 4.91% 21-Jul 151 4.92% 4.85% 4.91% 17-Mar 21-Apr 21-Jul 25 60 151 21 22 23