Problem 19.30. (Excel file)

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.")

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