Use the DerivaGem Application Builder functions to reproduce Table 19.2. (Note that in Table 19.2 the stock position is rounded to the nearest 100 shares.) Calculate the gamma and theta of the position each week. Calculate the change in the value of the portfolio each week and check whether equation (19.3) is approximately satisfied. (Note: DerivaGem produces a value of theta per calendar day. The theta in equation (19.3) is per year.)

Table 19.2 Simulation of delta hedging. Option closes in the money and cost of hedging is $263,300. Week Stock Delta Shares purchased price Cost of shares Cumulative cost Interest purchased including interest cost (8000) ($000) ($000) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 49.00 0.522 48.12 0.458 47.37 0.400 50.25 0.596 51.75 0.693 53.12 0.774 53.00 0.771 51.87 0.706 51.38 0.674 53.00 0.787 49.88 0.550 48.50 0.413 49.88 0.542 50.37 0.591 52.13 0.768 51.88 0.759 52.87 0.865 54.87 0.978 54.62 0.990 55.87 1.000 57.25 1.000 52,200 6,400) (5,800) 19,600 9,700 8,100 (300) 6,500) (3,200) 11,300 (23,700) (13,700) 12,900 4,900 17,700 (900) 10,600 11,300 1,200 1,000 0 2,557.8 (308.0) (274.7) 984.9 502.0 430.3 (15.9) (337.2) (164.4) 598.9 (1,182.2) (664.4) 643.5 246.8 922.7 (46.7) 560.4 620.0 65.5 55.9 0.0 2,557.8 2,252.3 1,979.8 2,966.6 3,471.5 3,905.1 3,893.0 3,559.5 3,398.5 4,000.7 2,822.3 2,160.6 2,806.2 3,055.7 3,981.3 3,938.4 4,502.6 5,126.9 5,197.3 5,258.2 5,263.3 2.5 2.2 1.9 2.9 3.3 3.8 3.7 3.4 3.3 3.8 2.7 2.1 2.7 2.9 3.8 3.8 4.3 4.9 5.0 5.1 = t + 52 (19.3) Table 19.2 Simulation of delta hedging. Option closes in the money and cost of hedging is $263,300. Week Stock Delta Shares purchased price Cost of shares Cumulative cost Interest purchased including interest cost (8000) ($000) ($000) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 49.00 0.522 48.12 0.458 47.37 0.400 50.25 0.596 51.75 0.693 53.12 0.774 53.00 0.771 51.87 0.706 51.38 0.674 53.00 0.787 49.88 0.550 48.50 0.413 49.88 0.542 50.37 0.591 52.13 0.768 51.88 0.759 52.87 0.865 54.87 0.978 54.62 0.990 55.87 1.000 57.25 1.000 52,200 6,400) (5,800) 19,600 9,700 8,100 (300) 6,500) (3,200) 11,300 (23,700) (13,700) 12,900 4,900 17,700 (900) 10,600 11,300 1,200 1,000 0 2,557.8 (308.0) (274.7) 984.9 502.0 430.3 (15.9) (337.2) (164.4) 598.9 (1,182.2) (664.4) 643.5 246.8 922.7 (46.7) 560.4 620.0 65.5 55.9 0.0 2,557.8 2,252.3 1,979.8 2,966.6 3,471.5 3,905.1 3,893.0 3,559.5 3,398.5 4,000.7 2,822.3 2,160.6 2,806.2 3,055.7 3,981.3 3,938.4 4,502.6 5,126.9 5,197.3 5,258.2 5,263.3 2.5 2.2 1.9 2.9 3.3 3.8 3.7 3.4 3.3 3.8 2.7 2.1 2.7 2.9 3.8 3.8 4.3 4.9 5.0 5.1 = t + 52 (19.3)