Effects of the Change of Delta

The following charts show the minute by minute price during the last ten trading days of the underyling security and of the call and put contracts composing my last delta neutral portfolio. The call and put charts have the corresponding delta values at the end of each trading day.





The following spreadsheet shows the price and the greeks of each option contract as they change as the undelrlying asset price and volatility change. The column named "theoretical" reports the theoretical contract price to be compared with the actual end of day price of the contract. The column named "effective" reports the effective delta resulting from the actual market price changes of both contracts and underlying stock to be compared with the theoretical delta.



Notice the considerable difference between the theoretical delta values and the effective ones at the end of 10/31/2006. The spreadsheet below show the position performance if I had used the effective delta values to build it. It would have been a gain of 44% instead of nothing. The following spreadsheet shows what actually happened.








This spreadsheet reports prices and greeks for AMGN. The agreement between actual values and theoretical values is good. The position lost money because AMGN was threading water.







The prices and greek values for UNH are in the spreadsheet below. Here again I can see a discrepancy between the theoretical and effective values of the delta.



If I had used the effective values the gain in this position would have been of 23% instead of 14%:




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