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The Lazy Man's Guide to Delta-Hedging


Something every options trader needs to consider.

In my last post on this topic, Why Delta Hedging Matters, I argued that an essential aspect of options trading is hedging away unwanted risks. For most traders, the unwanted risk is usually to directional price movement, or delta risk. This issue is important whether you're short one call contract or managing a book of hundreds of positions. Again, the motivation for hedging away some or all of your delta exposure is if the purpose of your trade(s) is to gain exposure to changes in volatility, rather than price.

Delta hedging is the practice of buying or selling options and/or the underlying asset in order to reduce the net deltas in an open position. For example, let's say I thought implied volatility in August XLE options was overpriced and that I therefore wanted to be short that volatility. (I don't have a view on XLE either way at the moment; this is just an example.)

The August XLE 45 call is at the money and has a delta of about 50; if I were short 2 of those calls, my net delta would be about -100. In order to delta-hedge the position, I'd buy 100 shares of XLE at the current price. Let's say I did all of those things at once -- bought the shares and sold the calls all at the same time, giving me a nearly delta-neutral opening position.

Because all options have some gamma -- because the delta of an option changes in response to changes in the price of the underlying -- that initial hedge is only the first step. As the underlying moves around over time, the net delta of the position will change as well.

The obvious response to any changes would be to adjust the hedge continuously, buying and selling the underlying asset tick-by-tick in order to stay completely neutral at all times. But that's not possible for several reasons: Transaction costs would eat up any profits, contract sizes might prevent sufficiently granular hedges, and the discrete nature of market prices means a continuous hedge is as impossible as counting all the real numbers using only the natural ones. Hedging continuously represents one extreme approach; the other extreme would be to never hedge, or to do so infrequently.

So the key to dynamic hedging is to navigate the 2 extremes, avoiding undue delta exposure on the one hand while keeping transaction costs as low as possible on the other.

Here are some methods of delta-hedging to consider. 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.

1. 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 2 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.
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No positions in stocks mentioned.

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