Simplifying option vega spreads

By , CEO of Volcube.

For options of the same expiration and the same underlying, there is a useful technique to simplify a complex position into its core vega characteristics. This technique is used by option traders with large portfolios to manage their risk and understand what lies at the heart of their position. It works best for options that have adequate time left before expiration; with perhaps a month or less until expiry, the technique is less effective for reasons that we’ll explain later.

A sample position

Suppose this is our position (delta-hedged), with the spot trading at $99.

99 calls. Flat position. 16.7 vega.  [At-the-money options].

101 calls. Long 1000 lots. 12.6 vega.

103 calls. Short 2200 lots. 9.3 vega.

105 calls. Long 800 lots. 6.7 vega.

107 calls. Short 250 lots. 4.7 vega.

109 calls. Long 300 lots. 3.2 vega.

We will use the simplifying technique to reduce this position down to its core vega component.

Option butterfly/condor spreads

The technique uses the fact that a tight, regularly-spaced butterfly (or condor) strategy often has very low vega. Butterflies and condors can essentially be viewed as one spread against another. Given that a spread is in itself generally lower risk than an outright, a suitable spread versus another spread, should be even lower risk. Take a look at the options in the example position. Let’s use the vega of the 99 strike (16.7) as the benchmark, since this must be the highest vega of any option in this month.  In vega terms, the 101 calls are about 75% ‘as big as’ the 99 calls, because their vega is 12.6. But take a look at the 99/101/103 call butterfly. This has only 0.8 vega (16.7 + 9.3 – (2 *12.6)). So it is very low risk in vega terms, compared to the at-the-money options alone.

So the technique involves sifting through the position looking for butterflies and condors that we can pretty much filter out, and then see what is left to get to the real meat of the portfolio. The idea is that the tight spreads are not contributing greatly to the overall vega, so we need to look through them to the outrights that lie beneath.

Simplifying the option portfolio

If you calculate the overall vega from this position (by summing the product of the number of lots long or short in each strike and the vega of the strike) you will find the position is net short about $2715 vega. This is equivalent to being short 162 lots of the 99 strike (ie this many at-the-money options will give you the same short vega position). But let’s see where this is really coming from by reducing the position down to its core components.

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The first thing to strip away from this position is the 101/103/105 call butterfly. This fly only has 0.7 vega, so it is not contributing greatly to the overall vega. Let’s temporarily remove 800 of these flies to see what is left. It is almost is if we ‘sell’ these butterflies back out. So we ‘sell’ 800 of the 101 calls and 800 of the 105 calls. We ‘buy back’ 1600 of the 103 calls, leaving us with…

101 calls. Long 200 lots. 12.6 vega.

103 calls. Short 600 lots. 9.3 vega.

107 calls. Short 250 lots. 4.7 vega.

109 calls. Long 300 lots. 3.2 vega.

Notice that the 105 calls have disappeared completely because we are now ‘flat’ this strike, having removed the butterflies. We can simplify this even more by noticing that the 101/103/107/109 call condor, although not perfectly regular, only has about 1.5 vega. Not insignificant, but not that big either. Let’s remove 200 of these condors as well, which gets rid of the 101 calls completely, leaving us with…

103 calls. Short 400 lots. 9.3 vega.

107 calls. Short 50 lots. 4.7 vega.

109 calls. Long 100 lots. 3.2 vega.

To spell this out, have ‘sold’ 200 of the 101 calls, ‘bought’ 200 of the 103 and 107 calls and ‘sold’ 200 of the 109 calls with this manoeuvre. So we are down to a short position in the 103 calls and then a small short position in the 107/109 ratio call spread. 50 lots of the 107/109 ratio call spread is in itself pretty insignificant (if we were short just 50 lots of the 111 calls as well, we would have another perfect butterfly to strip out), so we are really just left with the short position in the 103 calls.

Understanding the results of the simplification

If an experienced option trader was presented with the above portfolio and the vegas of the options, he or she could make this simplification in just a couple of moments. And it is a very useful short-cut because it works no matter how large the position gets. 1000s of option contracts can be ‘ignored’ because they are ‘butterflied-off’ , as they say. Once the trader has performed this simplification, he knows for example at an instant the optimal trade to reduce his risk. In this case, buying a few hundred of the 103 calls would work just fine. To the novice trader, this may not be obvious. He may think that to reduce the risk the trader needs to eliminate several strikes. But this isn’t always the case. In fact, sometimes adding to an existing position can actually reduce the overall riskiness (in terms of vega) of the portfolio. Again, this can be very counter-intuitive to an novice trader; the idea that buying a strike that one is already long, being a risk-reducing trade. The reason is that buying a long strike (or selling a short strike) may help in the overall context of the vega spreads in the book. In other words, the extent to which a position is nicely ‘butterflied’ can be improved by trading certain strikes in the same direction as the existing inventory.

Other things to note

A position can only be reduced so far. Often it will be reduced into one of the basic strategies. For example, the trader may reduce his position down and say “This position is basically short a call spread versus a long put”. What he means is that when all the longs and shorts are ‘netted out’ into the core outrights that are contributing most to the overall vega position, what is left is a some shorts to the upside (clustered around a strike) and some longs higher still (at another strike), with net longs to the downside (around another strike). Having a short hand summary of a complicated book can help the trader when quick decisions are needed or when he wants to just have a high-level understanding of his risk. Similar perhaps to a chess player who summarises a position as “I have a rook for his bishop but my king is a little exposed”, rather than noting the state of every piece and every square.

It has to be noted that when discounting low-vega butterflies or other strategies from a position, that one has to be sensible. If the entire position is a butterfly, we should not think we have no positional risk at all! All one can say is that the vega risk is probably low given the sheer number of options on the book. Just use some common sense. If a butterfly that one is ‘removing’ from the book makes up 60% of the vega and other risks, it is not sensible to discount it, since it is very important to the core of your position (which the whole point of this technique is to uncover).

This technique of spreading off options (using either butterflies/condors or other spreads such simple call spreads) is best suited to longer dated options. Towards expiration, things get a little too strike-specific for spreads or butterflies to really be dismissed out of hand. In effect, the ‘distance’ between strikes lengthens in vega-terms as expiry approaches. But for most options with more than a few weeks until expiration, this technique is a useful one to understand and practise.

Practising this option risk management technique and further guidance

It is very easy to practise this technique in Volcube. Simply login, start a game and make a few option trades in different strikes. Then use your Inventory pane and the Volcube Pricing Sheet to figure out your position per strike and the vega of the options. Even easier, you can use the Volcube Market Mentor to show the exact result of a simplification for your game. Simply call up the Volcube Market Mentor and press the “About My Inventory” menu item. This will show you the result of a simplification and you can compare your own simplification with Volcube’s!

About Volcube

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