From what I understand exotics traders utilize a technique known as barrier shifting (or bending) when pricing/hedging intruments with a barrier. For example if they sell a european digital call to a client with a strike of 100 the idea would be to actually charge them for the more expensive digital call with a strike of 98 and then dynamically hedge against the 98 strike over the lifetime of the contract. The idea then being that the bank gets the extra premium for charging at the 98 strike price and any windfall incurred if the contract expires between 98 and 100. This all to cover the risk (fron discrete hedging/transaction costs) of the position.My question is what is the advantage of doing this? Why not just charge a premium up front. For instance look at the p/l histogram and charge the client a premium that guarantees making money 95% of the time or whatever your metric is. Why obtain this premium indirectly in the form of barrier shifting? Is there something else that I'm missing here? Thanks for any insights.

The main advantage of barrier shifting (or bending) is that it smoothes your delta / gamma / theta when you are close to the limit. So if small, your dirac manages by itself and you can concentrate on more important stuff. When you have digital of 20 mio usd you are happy to have modelised a call spread to take into the gap risk and that is basically worth a lot of your product's price. When close to the limit some traders suppress their modelisation of the gap and actually buy the call/spread in the otc market when possible (providing you know on which stocks to buy it and the structure exists in the market).On your question on the premium i did not really get it as the bigger the gap the more expensive your options so it shows upfront.If you price a barrier shift where you make money 95% of the time, you probably won't get any deal and you still have the chance to lose big if the 5% chance are based on huge digits close to the limit. So statistical hedging does not make sense when it comes to specific igit risk i think.