The Lazy Guide To Delta Hedging

By: Condor Options Friday, July 10, 2009 1:04 PM

Symbols: AAPL, GOOG, RIMM, X

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I’ll refer to a "book," which should be understood as the set of all option contracts and positions that a trader wishes to hedge.

Time-based. Review the net delta exposure of the book at every time t and re-balance the hedge. The length of t will vary with the time to expiration of the options being hedged: a short out of the money contract expiring two years from now may require very little attention at first – only a weekly examination and monthly re-balancing, perhaps – but a weekly review may be inappropriate when that same contract has only a month until expiration.
Price-based. Since it is 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.
Fixed delta bands. When the delta exposure of the book exceeds a given level, re-balance 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 would want to keep your deltas for that trade roughly between -270 and 270.
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.

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