Use the DerivaGem Application Builder functions to reproduce Table 17.2
Problem 17.28. (Excel file)
Use the DerivaGem Application Builder functions to reproduce Table 17.2. (Note that in Table 17.2 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 (17.6) is approximately satisfied.(Note: DerivaGem produces a value of theta “per calendar day.” The theta in equation (17.6) is “per year.”)
Hint
Consider the first week. The portfolio consists of a short position in 100,000 options and a long position in 52,200 shares. The value of the option changes from $240,053 at the beginning of the week to $188,760 at the end of the week for a gain of $51,293. The value of the shares change from 52,200X49=$2,557,800 to 52,200X48.12=$2,511,864 for a loss of $45,936. The net gain is 51,293-45,936=$5,35...
Consider the first week. The portfolio consists of a short position in 100,000 options and a long position in 52,200 shares. The value of the option changes from $240,053 at the beginning of the week to $188,760 at the end of the week for a gain of $51,293. The value of the shares change from 52,200X49=$2,557,800 to 52,200X48.12=$2,511,864 for a loss of $45,936. The net gain is 51,293-45,936=$5,357.
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