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The image is from John C Hull Textbook titled Options, Futures and Other Derivatives ( page 407 - Ninth Edition).

The image is from John C Hull Textbook titled Options, Futures and Other Derivatives ( page 407 - Ninth Edition). The table above was obtained after computing the delta of stock price, shares purchased and interest cost.

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The labelling is indeed a bit confusing- this guy is normally very smooth!

Let’s focus on the weekly rebalancing column, here are the detailed steps.

1) Simulate the path of the stock price as per weekly frequency (20 time steps here as the option maturity is 20 weeks).

2) Calculate the delta of the option at each time step.

3) At the initial time, buy or sell shares, to hedge the delta of the option at time zero.

4) Readjust the delta hedge at each time step, buying or selling shares, depending on the change in delta from the previous step.

5) Generate the present value of the cost of this dynamic delta hedge.

Repeat the above precedure 1000 times, and calculate its standard deviation. Dividing this by the option price at time zero is the ratio you see in the table.

He is only after risk or volatility of the delta hedge. Average is not a problem as the average of the present value of the delta hedge would match the option price at time zero, if the black scholes assumptions are assumed to hold (e.g. constant volatility).

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  • $\begingroup$ I will attempt this. Your explanation is clear. Do u suggest the usage of VBA programming in the calculation? $\endgroup$ – Ash Raj Oct 31 '18 at 15:42
  • $\begingroup$ Vba or python would be great, but 1k paths with 20 sample paths is doable in spreadsheet. I would suggest try a couple of sample paths in excel and then code it in vba. You should be able to find python code for this online, but worth trying first. $\endgroup$ – Magic is in the chain Oct 31 '18 at 15:55

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