2. Price-Based

Since it's the changes in the prices of underlying assets that create the need for delta-hedging in the first place, there’s something intuitive about flattening out the deltas of your book in response to price movement of a certain amount.

So the method here is to re-balance the hedge whenever the underlying price moves by a certain amount. How to determine that amount is, of course, the whole issue: Some traders rely on intuition and/or subjective technical analysis to determine appropriate price levels, but those approaches raise more problems than they solve. A better approach would be to define a price range in terms of recent historical or implied volatility.

3. Fixed Delta Bands

When the delta exposure of the book exceeds a given level, rebalance the hedge. The level of the bands -- the amount of deltas above and below zero that you’re willing to tolerate -- will depend in part on the nature of your book and your risk tolerance.

A general rule of thumb here would be to determine a rough dollar amount that you’re comfortable losing due to price movement. Then, determine the number of points the underlying is likely to move in a given day (assuming you’re willing to adjust your hedge on a daily basis if needed), and divide your tolerable loss by that likely range to get your delta bands. In the example above, the expected daily range for XLE is about 1.10 points (about 2% at current prices).

So if your tolerable daily loss was $300, you'd want to keep your deltas for that trade roughly between -270 and 270.

4. Variable Delta Bands

The fixed-band approach isn’t sensitive to changes in gamma or implied volatility. That’s important because, all else being equal, a book with substantial short gamma has more risk: As the underlying moves further against you, your deltas will increase adversely as well.

By contrast, a book with substantial long gammas can afford to let the underlying run since it will become more neutral during an adverse move. The point here isn’t that traders should be short or long gamma; it’s that the hedging method employed should account for these risks wherever possible.

The chart below, from the Zakamouline article linked below, plots a delta band for a short butterfly spread with strikes at 80, 100, and 120. As you can see, the hedging bandwidth moves in line with the absolute value of the portfolio gamma, and reaches a fixed level as gamma approaches zero.



5. Academic Models

There's a substantial academic literature on optimal techniques for delta hedging, and some of it even deigns to consider whether the techniques under discussion could ever be deployed in the real world. (I’m calling this the lazy guide to delta hedging precisely because there are no formulas involved. Unless you’re managing a very large book and/or institutional money, you needn’t necessarily bother with the ivory tower approaches. If you do want to geek out, the bibliographies in the links above offer ample opportunity.) I found Zakamouline 2006 helpful, and chapter 4 of Volatility Trading by Euan Sinclair offers a thorough and accessible survey of this topic.

I've intentionally avoided endorsing one method over another, because, as is so often the case in options trading, the appropriate method for an individual will depend on her book, her experience, her risk tolerance, the nature of her strategy, etc.

The smart way to approach the topic of delta hedging isn't as a search for some one, right answer, but rather for the best fit given your situation. One issue I haven’t discussed yet is the matter of books with multiple underlying assets: A trader holding options on Google (GOOG) and US Steel (X) shouldn't treat their deltas equally.

It’s not a problem to hedge at the level of individual products, i.e. buying/selling the relevant shares of GOOG and X as needed. But for larger books, this quickly becomes less desirable. One solution to this problem is to beta-weight individual assets to some smaller set, i.e. weighting Apple (AAPL), Google, and Research in Motion (RIMM) options to the NASDAQ 100 and hedging with index products.

Inexperienced traders sometimes tend to pay too much attention to up-front transaction costs and minimize the costs of carrying unhedged risk. Whatever method you use, the most important thing is that you use one. Delta hedging is a fairly advanced topic, but it’s something that every options trader needs to consider.