I put together a simple simulation of delta hedging a set of options with an underlying and it seems that the fluctuations of the price still seem to affect the final outcome. The reason, I understand it, is because when we rehedge, we assume that $\Delta_{S}=1$ but we don't factor in the fact that the price keeps changing. Is this a normal consequence of delta hedging practices?
Incidentally, my approach to keeping track of the amount of underlying bought or sold is to keep information related to total underlying position and the recalculated price which is
- If position is increased, we recalculate the price based on the increased position, i.e. average out the prices.
- If position is decreased, we keep the entry price the same, reduce the number of underlyings and calculate the p/l of the underlyings we bought/sold as cash.
So, another question - is this the right way to recalculate the portfolio position?