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Scalping Gamma

In my last article on option trading I suggested that longer term implied volatility looked rich while short term volatility looked cheap.  The strategy that I suggested to extract this value was to buy short-term ATM puts, sell 1 year or greater out of the money puts, and delta hedge the position.  I called this getting “Long Gamma and Short Vega”.  There were many comments related to simpler strategies on the VIX or via variance swaps for the lucky Europeans who have them to trade, but I maintained that I believe the strategies can be very different because of the flexibility and specificity that options provide.

When discussing how to mitigate gamma losses, I used Yahoo as an example, but this time I will explore the S&P 500 because it looks even more ripe for this trade idea.  The first thing we need to examine is the option implied volatility skew:

S&P 500 1 Year Versus 1 Month Implied Volatility Skew

There are two things that you should notice about these curves.  The first is that 1 year implied volatility is trading at higher levels than 1 month implied volatility.  The second point is that the curves exhibit “reverse skew”, which simply means that the lower strike prices trade at higher implied volatilities than at the higher strike prices.  This gives us two takeaways: 1) If we are selling options we would prefer to sell longer dated options (higher implied volatility) 2) when we are buying options we would prefer to buy them at higher strike prices (lower implied volatility).

With these two things in mind comes the strategy that I originally suggested: Long Gamma, Short Vega.

Now that we have the strategy down, let us dissect why it makes sense.  From my previous post on mitigating gamma losses, we know that options exhibit large gamma at the money close to expiration.  Let us consider a purchased put option on the S&P 500 with a strike price of $1,150:

Gamma spikes dramatically when options are close to expiration and the underlying trades near the strike

Gamma spikes dramatically when options are close to expiration and the underlying trades near the strike

Gamma is what whacks option sellers silly because a written option with a small loss can turn into a very large loss when the option nears expiration and the underlying spikes into the money.  In the case of being long gamma, we are happy to see the underlying move rapidly because that means that there is more of a chance that our long option position will end up far in the money.  If we are long an option and gamma scalping, we are also happy to see the underlying move quickly because we lock in large gains.  This can best be understood with an image:

Because of a positive gamma, the delta-hedged long put option gains in up and down scenarios

Profit & Loss from a Delta-Hedged Long Put position rebalanced at the 1,100 S&P 500 level

The important piece to keep in mind when examining the P&L of the delta-hedged position is to remember that you re-balance, or hedge your delta to zero, at discrete points in time.  In this example, we assume that you re-hedge when the S&P 500 is at 1,100.  The profit of $13 occurs when the S&P 500 falls to 1,000 before you re-balance your hedged position.  Likewise, the profit of $15 occurs when the S&P 500 rises to 1,200 before you re-hedge your position.  This is just an illustrative example, but it shows that the option gains more when the market falls than the long stock position  loses.  This happens because the option’s delta gets closer to negative one as the option moves further in the money while your delta hedge position remains constant at 65% of the option notional.  In this position, we crave realized volatility for the profitability of the delta-hedged long option strategy.

If we pair a long position in the ATM short-term option, which has a very high gamma, with a short position in an out of the money long-dated option then we still end up with a net positive gamma.  This position will only flip-flop to a negative gamma when the market moves towards the out of the money written strike.  Therefore, we can scalp gamma in the short-run while having an overall short vega position on longer-dated written option.  I will let this idea sink in and leave short vega positions for another time.


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12 Responses

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  1. NGB says

    I was thinking about other ways to profit from the Skew, suppose I write a 95 one month put (I am selling 17% volatility), then I buy the 110 one month call (buying 13%), then I delta hedge the position daily. From what I’ve learned here if the realized volatility is higher than the implied volatility the long option position will make money and the short one will lose it, the opposite will be true if the implied is higher than realized. The point here is that in theory I could make money no matter what happens with volatility, which doesn´t make sense. So clearly I am missing something here, otherwise the mere existence of a strike skew will give an opportunity for arbritage, what am I missing? Congratulations for your blog, it is by far the best blog in finance related topics I have seen.

  2. SurlyTrader says

    When you are looking at options, it is actually much easier to look at two options of the same maturity, because then you are just concerned with your delta and gamma – especially when they are short term and the vega is small. It all comes down to managing the greeks. I replicated your theoretical situation in Bloomberg and it shows that i sold 1 put option at 1075 and bought one call option at 1240 so that my P&L is basically 0. In this situation, the put option has a higher negative gamma and a higher negative vega. This means that, overall, you want volatility to come out *lower* when you are delta hedging. That lower number is function of both the call and the put. If volatility comes in higher you will make a little bit off of your long call position, but you will lose much more from your short put position. The interesting thing about using options of different time periods is that I can have a vega position that is different than my gamma position and that is what I was talking about in the article. A long dated option has a lot of vega exposure but little gamma exposure whereas a short dated option has a lot of gamma exposure and little vega exposure. Check out the picture below to see your strategy’s greeks. Thanks very much for the kind words and spread the word about surlytrader.

  3. Randy Woods says

    This also illustrates why you want the market to go to your short strike at expiration. If you delta hedged the above by shorting the underlying, that becomes another profit engine, provided the market doesn’t blow thorough your short strike by several handles. You’ll take some heat as the market approaches your short put but eventually the decay will happen.

  4. EuropeTrader says

    It seems to me that you are misunderstanding the volatility skew…in stocks, OTM puts have always higher implied volatility than OTM calls. (The opposite only happen during takeover bid, when the risk is on the upside, but thats a special case). Having OTM puts higher implied volatility does not mean it should not be bought.
    You wrote “when we are buying options we would prefer to buy them at higher strike prices (lower implied volatility)”… this is not true. If the stock goes down, you want to be long the put, in other words, you want to be long the convexity. The profit will be quadratic and increase tremendously if the stock goes far down and fast (even better). Why will it be better than being long the OTM call?…well, because once your underlying has moved 5 or 10% on the downside, you can say goodbye to your OTM call. You will indeed make a bit of money with it, but its gamma will vanish as you go down.
    Trading OTM puts and calls are not easy at all in practice…and people who think it is, often lose big time in trading, or if they make profit is luck!…and they dont realize that is luck (even worst!)
    Its all about market expectation…You think the OTM puts are cheap? well buy it, hedge it…as you go up, people might bid it up even more…its all about skew curve dynamic and the expected forward volatility.
    Buying OTM call (hedged) as you go up can be a nightmare…if the realized volatility is low, you will lose on your vega…if that happen, you better let your delta run to offet this loss…
    There are many different situation to be explained…
    The first question you might ask yourself is: what is the skew? why? what does it mean to buy a OTM put with an implied vol of 30% if the ATM put has an implied vol of 25%? what do the stock have to do to break even? why are people buying the OTM put if they can buy the ATM or OTM call for lower implied volatility?

  5. SurlyTrader says

    It seems to me that you misunderstanding my writing. It is better to buy options at higher strikes, not just calls but puts as well because you are buying at an implied volatility that is lower. I would much rather buy an ATM put than buy a put that is 10% out of the money with a steep skew. I absolutely do not think out of the money puts are cheap, I say they are expensive and you would understand that if you read any of my posts. I am consistently selling out of the money puts as an alpha generating strategy. I infrequently buy OTM options, calls or puts so I don’t know where you are coming from with your statements. In general I don’t really understand your comments.

    Bottom line, I prefer to buy options at lower implied volatilities, and I generally buy options at the money or in the money. I sell out of the money puts consistently because I think that the steepness of the skew, which is a result of jump diffusion on the downside, is too high for the downside risk – meaning that people are paying too much for downside protection even given events such as 2008 and 1987. I usually only sell call options when it is part of a short strangle or short straddle position. BTW, convexity is used with bonds and fixed income derivatives, not with equity derivatives. Gamma is convexity in the equity world.

  6. EuropeTrader says

    Ok, I got your point although I found it a bit confusing. You wrote in the same paragraph: “. It is better to buy options at higher strikes” and ” I infrequently buy OTM options, calls or puts”

    Another question, if you are long the Put Spread (so Long ATM put, and short OTM puts = Long cheap vol, short expensive vol), how do you manage your risk/position as the stock goes down (fast)? We all know that being long the put spread give you a good gamma/theta ratio…nice if the market is ranging but what about accelerating downward movement? Being gamma short/vega short/vanna long on the downside can be a nightmare.

    Can you argue your point “steepness of the skew is too high for the downside risk” & “people are paying too much for downside protection”? …it is a quite powerful statement here…sometimes its right but saying it as a general rule is quite dangerous…Don’t know if Derman, Taleb or Alexander agree with you on that point.

    Are you looking at local volatility (forward volatility per strike) when you are trading option? to better assess the level of implied volatility of the option.

    How do you dynamically hedge a risk reversal position? Do you believe on sticky strike/sticky delta or customized model?

    I would be interested to hear your point.
    Thanks for your quick response. Always nice to talk with someone who has a different opinion of trading.

  7. SurlyTrader says

    Sorry for the delayed response. I think you would benefit by reading my previous post “Do Black Swans Negate Option Premiums?” as well as reading the research piece by Oleg Bondarenko that I refer to. That might answer quite a few of your questions.

    With regards to buying a put spread: I would buy a put spread if I believed that the equity market would fall only a certain amount, say 10% when I bought a 100/85 put spread. If I thought that the market was going to fall precipitously then I would only buy the ATM put. One mistake people often make is to try to “cheapen” a trade. You are ALWAYS giving something up when buying a spread position as well as when you sell a spread position.

    I do look at local volatility.
    I do not believe in sticky strikes, but I realize that the limitations of any model will cause a slippage in my delta hedging. There is not a perfect solution, but if there is a systematic mispricing then it should not matter over time. All models are wrong, but useful.

  8. Tanjtrader says

    Hi there,

    If i may, you are what we call a Tanj’.

    Thx for your blog, i lear a lot!


  9. EuropeTrader says

    ” If I thought that the market was going to fall precipitously then I would only buy the ATM put” … believe me, that is not the optimal put!…if you think the market will move down sharply and fast, the optimal put is the put that has the greatest vanna in order to get the highest leverage…certainly not the ATM put which has indeed the highest gamma/convexity at some point but that is it…last thursday and friday was a perfect example…ALL market participants were buying those puts during the slide…

  10. SurlyTrader says

    I agree with you, if you absolutely know when crashes are going to occur. But scalping gamma is about the positive or negative gamma of the position, not the exponential increase in a far out of the money option price when a crash occurs. Preparing for “black swans” is not a long-term strategy and also why Taleb no longer has a hedge fund.

Continuing the Discussion

  1. Trading Gamma | SurlyTrader linked to this post on March 21, 2012

    […] that no longer needs to be the case.  For a primer on Gamma trading, I would suggest reading  Scalping Gamma and Long Gamma, Short […]

  2. The Difficulty in Adding Vega Exposure – Tenor | SurlyTrader linked to this post on August 7, 2012

    […] If you want the cleanest and simplest way to add volatility or vega exposure by using options, you would generally buy a straddle.  A straddle will purchase the same amount of calls as puts with the same strike, time to maturity, and the same expiration.  With this position, you basically want the market to move a lot in one direction.  A pure long volatility strategy would delta hedge the straddle so that you can capture all large up and down moves in the market over the duration of the position (by scalping gamma). […]

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