I have two questions.1. Is the Whalley WIlmott hedging formula valid for hedging a portfolio of vanilla european options?2. How does one account for multiple contracts? For example, if we assume that there are 100 contracts that are being traded then the whole bandwidth quantity only gets scaled by 100^{2/3}. 3. May be the formula needs to be considered for single contract notional and multipled by contract size?Thanks.

If I understand the question correctly, here is my interpretation:1. I think you have to be careful about combining for a portfolio of options. The no-transction region changes with maturity and in-the-moneyness of the option. I would imagine that one would have to test for being within the transaction region on an option-by-option basis, and then to net the overall rebalances in such a way that each individual option meets its transaction-no-transaction requirement. Remember, if a hedge is outside the region, it is to be rebalaced to the theoretical delta; if it is within its region, it is to be left alone.2. For multiple contracts on the same option, you look at the delta per option and the no-transaction region per option. Then scale the results for multiple contracts. The formula assumes proportion transaction costs (here its lambda) and so is invariant with scale. The formula cited is the distance of the no-transaction boundary to the theoretical delta.3. Yes, as above.BM

Thanks.