Greeks - Delta and Gamma Explained

let's use SPY trading at $108.20 with 11 days to expiration....the following Greeks for a Long Nov 109-strike Call are :

Delta : +0.41
Gamma : +0.1
Theta : -0.06
Vega : +0.08

a quick reference to this and then we move on to more specific Greek talk..

the above is a Bullish directional option position, which was established by paying a premium of ~$1.91 or $191 for 1 contract size.. this is evident from Delta, which is +ve 0.41.. this also represents the position's biggest risk..

Delta Risks
why is this +ve 0.41 delta, the biggest risk? for one primary reason; if SPY moves up or down 1point, this position gains or loses $41 (0.41 x 100)respectively. this is a 21.5% fluctuation in the P/L; a significant % by any measurement.

therefore, before anyone goes Buying single directional options, whether Long Calls or Long Puts, the trader MUST understand Delta risks... which is most prevalent for Long Calls and Puts.

Gamma Risks
a +ve gamma is always associated with any Long options. remember, +ve gamma has nothing to do with directional bias. this means, one can Long Call or Long Put, such positions will always yield a +ve gamma. as long as you BUY an option, you will be +ve gamma; and conversely, as soon as you are Short(sell or write) an option, you will be -ve gamma.

gamma is best explained vis-a-vis delta. they are a pair of Siamese twins...because delta of an option position changes ONLY because gamma changes it. if gamma is 0(zero), no amount of movement of the underlying will change the delta value of that option !!!

in this example above, this Long SPY 109 Call assumes a +ve 0.1 gamma risk. how so? recall that gamma changes delta. gamma either makes a delta bigger or smaller. in this example, if SPY moves up 1 point, this Long 109 Call delta becomes +ve 0.51 (0.41 + 0.1) and if SPY drops by 1 point, the same Call option value will drop by +0.31 (0.41 - 0.1). of cos, this is a simplified calculation, becos gamma itself changes as SPY moves about. but we will keep it simpler here.

hence, if SPY moves up by 1 point, gamma helps the 109Call value tremendously by pumping the delta value up by ~24%(from 0.41 to 0.51),making this an even greater delta risk play. similarly, if SPY drops by 1 point, the option value will drop by ~23%..

therefore, if you are very bullish and decide to purchase a Long Call option, you want a large enough +ve gamma, to help you increase your +ve delta. BUT you had better be right on your directional bias, because if you were wrong, a large +gamma can also quickly erode your +ve delta of your Long Call option position, making it less sensitive of subsequent upward price movement of the underlying.

this, in a gist, is what gamma risks is all about...