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As far as I understand, most investors are willing to buy options (puts and calls) in order to limit their exposure to the market in case it moves against them. This is due to the fact that they are long gamma.

Being short gamma would mean that the exposure to the underlying becomes more long as the underlying price drops and more short as the underlying price rises. Thus exposure gets higher with a P&L downturn and lower with a P&L upturn.

Hence I wonder who is willing to be short gamma? Is it a bet on a low volatility?

Also, for a market maker in the option market, writing (selling) an option means being short gamma, so if there is no counterparty willing to be short gamma, how are they going to hedge their gamma?

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Re the point on realised vs implaied volatility, straddle being an option of choice..post the initial delta adjustment how does realised vol traslate into cashflows through delta adjustement?..since strddle is gamma neutral! –  user2208 Mar 26 '12 at 12:40
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6 Answers 6

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Being short gamma simply means that you are short options regardless of whether they are puts or calls.

The most common type of investor that is willing to be short gamma is someone who sells options, also known as a premium collector.

These investors commonly use strategies such as short puts, covered calls, iron condors, vertical credit spreads, and a few others.
These strategies are typically referred to as income generation strategies.

They offer the investor a return known in advance, in exchange for the risk of being short options. Frequently these types of income trades have have a probability of success over 80%. Clearly there is significant risk associated with a probability of success that high, so approach with caution.

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I might be misunderstanding your question. My thoughts:

  • being short gamma is being long volatility

  • your comment re gamma increasing regardless of direction only holds for ATM options. For ITM options, being short gamma is being long the underlying. For OTM options, being short gamma is being short the underlying.

Some graphs:

  • Below, except as noted, the underlying is at 1, the interest rate is 0%, and the expiration date is 1 year.

  • The gamma of an ATM call as its volatility varies from .05 to .15:

    Plot[bsgamma[1,1,1,0,v],{v,.05,0.15}]

enter image description here

  • The gamma of a .95 ITM call as the underlying varies from .95 to 1.05:

    Plot[bsgamma[x,0.95,1,0,.10],{x,.9,1.1}]

enter image description here

  • The gamma of a 1.05 OTM call as the underlying varies from .95 to 1.05:

    Plot[bsgamma[x,1.05,1,0,.10],{x,.9,1.1}]

enter image description here

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Thanks for your answer. I think you misunderstand the point when you say: "your comment re gamma increasing regardless of direction only holds for ATM options. For ITM options, being short gamma is being long the underlying. For OTM options, being short gamma is being short the underlying." I mean that when you are short gamma you're exposure to the market (in term of beta) increase regardless of the direction, but I don't mention the gamma variation here. My question is not really about options, but more to get a practical understanding of what is gamma, and who is willing to buy or sell it. –  jules Apr 11 '11 at 8:56
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"being short gamma is being long volatility" - false. short gamma = short vol. "For ITM options, being short gamma is being long the underlying. " - false (eg short call (itm or otherwise) is short the underlying). –  glyphard Apr 22 '11 at 21:52
    
@glyphard - slightly incorrect, you can be (fairly) gamma-neutral while having a net volatility position - eg a straddle/strangle. Also, a short put is short gamma but long underlying. –  Akshay Aug 23 '11 at 21:05
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Short gamma is a bet on volatility (expressed as hedging costs) not getting too large.

The key concept here is that you get paid to be short gamma. Consider that any option is sold for a bit more more than its intrinsic value (the extra bit is often called volatility value.). If nothing moves, then the option ultimately expires precisely at intrinsic value, netting the seller profits equal to the volatility value.

Thus, one is willing to be short gamma if one thinks the "rent" is sufficiently high. Obviously this can involve high tail risk, but it is otherwise a steady money-maker. Indeed there are many cases of people backtesting options strategies without including tail events and believing they have found some kind of holy grail.

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The only thing I'd add to this is that gamma is typically the tail wagging the dog in these trades. Trades that invole short gamma, particularly when described in terms of "rent", are attractive because of being long theta and willing to risk being short vol. Gamma is seldom a consideration because it's effects are not very pronounced until very close to expiration. The exception here is clearly if you are using close to expiry options as a hedge for the delta of a portfolio. –  glyphard Apr 22 '11 at 22:00
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You are absolutely right to point out that most proactive participants in options markets prefer to be long gamma, and it is typically reactive market makers who take the opposite side of their trades. While the typical options trader (I find it difficult to call anyone trading options an "investor") does not hedge his position, market makers will attempt to dynamically hedge an entire portfolio of options. In addition, covered call writers (also known as call overwriters) are a major source of gamma to the market, particularly for individual stocks.

Most market makers will immediately delta-hedge with the underlying, and will typically seek to offset the other Greeks of that option (most importantly, Gamma and Vega) by buying other options on the same underlying at more attractively priced strikes and/or tenors. Failing that, some more sophisticated market makers, or market makers in less liquid options, will put on an inexact hedge using options on a closely correlated underlying with more liquid options, or with ETFs or index options.

Market makers are typically paid for this service via the negative volatility risk premium (see Bakshi and Kapadia [2003a]). In other words, the P&L from a typical delta-hedged short gamma (short options) position is positive. However, partly due to the influence of call overwriting, which is more common for individual stocks, and partly due to the ability to diversify away some idiosyncratic volatility, the volatility risk premium is much greater in index options (see [Bakshi and Kapadia 2003b]). Some active options traders also attempt to exploit this difference via dispersion trading.

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If you get paid enough theta it absolutely makes sense to be short gamma. And the closer to expiration, the faster the time-value flees. Most of the time, most people would prefer to be gamma long though. It's simply a safer bet because of uncertainty: unexpected events can seriously damage your book if you're short vol.

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Short gamma is being of the view that realized volatility would be less than the implied volatility for the period in which an option is valid. So if you think realized volatility in the future would be consistently lesser than implied volatility at present, then you'd be short gamma.

The premium one would receive by selling an option (call or put) is a proxy for the implied volatility of the underlying (forward underlying, to be precise, if you take into account stochastic discount rates). Call this (single) cashflow I.

The amount one would lose in a delta-neutral short option position would be due to constant adjustment of the hedge (as the underlying keeps moving). This is roughly 0.5 * gamma * (change in underlying)^2 for each time step. Call the discounted sum of these delta-adjustment based "realized" cashflows R.

So, a short gamma investor is hoping that I-R >= 0

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Re the point on realised vs implaied volatility, straddle being an option of choice..post the initial delta adjustment how does realised vol traslate into cashflows through delta adjustement?..since strddle is gamma neutral! –  user2208 Mar 26 '12 at 12:40
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