Using the Black-Scholes pricing function in Excel, calculate how sensitive IBMs March 110 call price is to changes in stock price. How much does the call price vary for $0.50 changes in IBM share price when the option is at the money (assume stock price=$110), in the money (assume stock price=$115), and out of the money (assume stock price=$105)? What does this sensitivity analysis tell you?

Exhibit 1 ITO'S DILEMMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft Returns (In Duke Energ IBM Microsoft Week No. Prices Duke Energ IBM Close Close Date Microsoft Close 1 2 3 4 5 6 7 8 9 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 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 115.47 120.34 120.15 128.69 133.30 129.19 124.70 123.58 112.35 115.72 108.80 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% 41.06 41.96 36.25 41.10 34.83 36.16 38.24 37.33 41.02 41.16 42.27 Weekly Sigma of Returns Annualized standard deviation of returi 6.34% 45.75% 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 1.30 2.25 40 42.5 45 4.30 3.90 2.40 2.70 1.25 5.30 4.80 3.30 0.75 2.40 Duke Energy 42.27 42.27 42.27 IBM 108.90 108.90 108.90 Microsoft 55.19 55.19 55.19 100 110 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 7.00 10.50 15.60 120 13.90 50 55 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 60 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% 17-Mar 25 4.85% 21-Apr 60 4.91% 21-Jul 151 Exhibit 1 ITO'S DILEMMA Weekly Prices and Returns for Duke Energy, IBM and Microsoft Returns (In Duke Energ IBM Microsoft Week No. Prices Duke Energ IBM Close Close Date Microsoft Close 1 2 3 4 5 6 7 8 9 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 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 115.47 120.34 120.15 128.69 133.30 129.19 124.70 123.58 112.35 115.72 108.80 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% 41.06 41.96 36.25 41.10 34.83 36.16 38.24 37.33 41.02 41.16 42.27 Weekly Sigma of Returns Annualized standard deviation of returi 6.34% 45.75% 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 1.30 2.25 40 42.5 45 4.30 3.90 2.40 2.70 1.25 5.30 4.80 3.30 0.75 2.40 Duke Energy 42.27 42.27 42.27 IBM 108.90 108.90 108.90 Microsoft 55.19 55.19 55.19 100 110 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 7.00 10.50 15.60 120 13.90 50 55 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 60 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% 17-Mar 25 4.85% 21-Apr 60 4.91% 21-Jul 151