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Fading Gamma

As an option trader, you will find that options provide much more flexibility than merely making bets on price levels.  Options change in price due to changes in the underlying (duh), the implied volatility, the passage of time, and even changes in interest rates.  When looking at options with short periods until expiration, changes in the underlying price take center stage (delta) as well as the speed of the changes in the option price due to changes in the underlying price (gamma).  Gamma in the equity world or convexity (same thing) in the bond world are truly the heart of all derivatives transactions.

For background material on Gamma trading might I suggest:

The trickiest part about trading gamma is that it can change dramatically as the underlying price moves.  If you believe that the implied volatility being priced into short dated options is too low given possible market risks, you might want to be long gamma.  By being long gamma, you really are betting that realized volatility will be higher than the priced in option implied volatility until the expiration of the option.  If we look at a simple example of the $140 strike April 21 puts on the SPY, we can see that the priced implied volatility is about 14.35% or 14.35%/sqrt(252) ~ .90% movement per trading day:

IVB - Implied Volatility Bid, IVA is the Ask

If you purchase this put and sell enough SPY shares to make the trade delta neutral, then you are placing a bet on the how much SPY is going to change more than the predicted .9% per day.  As you saw in the Trading Gamma post, your profit can be estimated with some simplicity.

The issue is that delta is not the only greek that changes for the option with changes in the underlying SPY price.  There is actually a third order derivative which is often refered to as “Speed” which would tell you the change in gamma for a point change in the underlying SPY price.  In the case of the $140 strike April put option in question, you can see that gamma changes dramatically:

The obvious response is: “If I want to be long gamma then I assume that the market will be dropping.  If the market is dropping, I want my positive gamma exposure to be large even at lower strikes!”  If you were to just purchase the one, $140 strike put then you would be disappointed as the market dropped to 135 and below.

The answer is to buy more options at different strikes.  If we add a $132 strike put along with a $148 strike put, we can see that we have significantly changed our gamma profile:

There is no one “right” answer for establishing a long gamma or a short gamma position, but this does remind you that you must always think in multiple dimensions when trading options.

 

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2 Responses

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  1. Mike says

    Speed huh? Maybe they should just call it Meth. I kid…

    Nice article.

  2. Praetorian says

    I have one comment and one question. The comment is that your idea seems to me like starting to replicate a long variance swap, where you buy several options at different strikes in certain proportion and then delta hedge, if course since we are not selling anything to clients like a bank, the replication doesn’t have to be perfect, just good enough to obtain the effect we are looking for.

    I am a little bit confused about your definitions of trading gamma and vega, since both involve the outlook of realized volatility vs current implied volatility. As you mentioned in one article it is even possible to be long one and short the other. The question is, how would you define the difference between trading gamma and trading vega?

    Great article as usual.

    Thanks



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