Gamma is the largest risk in selling options which is the reason that the Gamma symbol has been chosen for this website. In fixed income it is called convexity and in Calculus/mathematics it is called the second derivative or the rate of change of the first derivative. Gamma tells us how much our delta, or exposure to the underlying, changes with a small change in the same underlying. You can read more about mitigating gamma losses in a previous post, but for now I just want to touch on one subsection of the gamma story.
Gamma changes as options get close to expiration. If you sold a put option with a strike of $50 and the option is trading at $55 with a few days to expiration, chances are that the delta of the option is close to zero. The problem is that the delta of that option moves quickly to -1 as we fall to $50 on the stock price, which implies that the gamma spikes as we get close to the strike. The point is that both delta and gamma change rapidly as an option gets near to expiration. What this means for a trader is that a written option that seems like a clear winner can quickly turn into a loser when the market moves quickly.
A few recommendations for the option sellers with regards to short-dated options:
- Gamma is not a fixed value. Do not fool yourself into thinking that you are safe because your negative gamma is small. More sophisticated traders will shock their option positions on a nightly basis.
- Don’t be greedy. If you sold an option for $1 and the option is currently trading for $.05-$.25 then seriously consider closing out the position. Regardless of the calculated implied volatility on the short dated option, it is often not worth the dislocation risk to hold that position to expiration.