If an option is sold and is being hedged with other options with different conditions then merely matching the two opposing deltas will not fully hedge the written exposure. This is due to the fact that the values for the written and purchased options will not change by the same amount. In order to hedge correctly, the gammas of the long and short positions need to be equal. This is because a small change in the asset value will cause a large change in the option value. The greater the volatility, the flatter the gamma curve.
Higher volatility spreads out the delta and it has a similar flattening effect on gamma.
As with delta, a directional view on volatility requires the appropriate gamma position. A positive gamma is required if volatility is expected to increase, and a negative gamma if volatility is expected to decline. Case Solution 2 Calculate the required number of puts needed for each separate put purchase, and calculate the associated cost for each separate purchase. Calculate the value of your portfolio at August 31, and calculate the value of each of the three possible option positions. Calculate the initial cost of the position, final net cost of the position as a percentage of the initial portfolio, and the percentage fall being insured against in each case.