Gamma is a greek term that identifies the rate of change in a delta. In essence, it is the delta of the delta. Why is this important? It is significantly important because gamma is a dynamic animal and is most sensitive as an option nears the end of its “life”.

Think of it as a dying entity, a warrior lying in the battlefield gasping for his last breath, lashing out, striking at anything that comes close. This is the very essence of the term gamma. The life of an option is limited. It either ends up in-the-money (ITM) or out-of-the-money (OTM); no two ways about it. That said, if the option ends up ITM, the delta is 100; same as the underlying. If on the other hand it ends up OTM at expiration, it is left for dead, expiring worthless, left behind, reduced to nothing but mere memory; no epithet to speak of laid to rest in a paupers grave.

For this very reason there is a need to understand the nature of the beast. Gamma may cause a false or erroneous number with regards to a position which in turn may lead to unnecessary hedging. As an option approaches expiration, an ITM option has similar characteristics of the underlying and the actual delta is reduced to mimicking stock if and only if, it is ITM. The option begins to trade at or close to parity. If the option is OTM, the delta is in effect zero. It needs to also be understood that, realistically, the delta is a probability with regards to being either in-the-money or out-of-the-money at expiration. The closer the underlying trades to the strike in question, the greater the rate of change in the delta at the point in which the underlying trades through the strike. As the life of the option is nearing, the delta wanes. This is why gamma can seemingly become explosive. Options that are OTM have a very low delta especially on the days leading up to expiration where as an option that is ITM is in effect trading the same as the underlying. The difference and dynamics come into play at which point the stock trades through the strike itself. If an option has a delta of close to zero and then changes to a delta of 100 and is trading at or close to parity with the underlying, gamma tends to explode and can wreak havoc on a position.

Here’s an example.

With eight days left until May expiration BRUN is trading at $28.30.
May 28 calls are trading for 0.39 and the gamma is 0.59 and the delta is 0.35.
With 3 days left until May expiration BRUN is trading at $27.94.
May 28 calls are now trading for 0.12 and gamma has nearly doubled, now at 1.10 and the delta is now 0.44.
If a trader is long 100 of the calls his delta would be reading long 4,400 shares while the gamma is 11,000. If the trader were on the other hand short -100 of the May 28 calls, the deltas would be -4,400.
The 28 call is .06 OTM and has a good chance of expiring in the money.

The reality is that this close to expiration, the call only has intrinsic value if the stock trades over $28. If the stock does trade up over the $28 to say the $28.25 level, we know at expiration the value of the option is 0.25 and the trader will be long or short 10,000 shares of BRUN depending if long or short the options. Under $28 the calls are worthless and he will not be long or short any shares of stock with regards to the May 28 calls. Setting the front month volatility to zero removes any false readings in deltas as well as in gamma. Understanding the dynamics of options in relation to front month deltas and gamma is important when trading positions as well as understanding proper risk management. It is necessary to grasp the significance of these dynamics in order to avoid unnecessary hedging as well as the resulting position implications at expiration and what the post expiration positions may be.

Terms:

Gamma: The rate of change in the delta of an option in relation to the rate of change to the underlying.

Delta: The rate of change in price of an option in relation to the underlying.

Intrinsic Value: The value of an option in relation to the underlying regarding being in-the-money.

Extrinsic Value: The value of an option in relation to the price being over parity; the excess value in the option.
 

Ross Barnett Terry, Contributor