[Derivatives] - The Greeks

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Please help me about the meaning of gamma. I cann’t have a clear view about this.
Why is gamma MAX when the option is at the money and closes to marturity? Many times put questions on this, find the path then forgeting all :(
 
Gamma is the derivative of Delta with respect to spot. In plain english, it’s how much delta changes per change in spot price.
so
Delta: change in price of the option per change in price of spot
Gamma: change in delta per change in spot
To answer the “Why is gamma MAX when the option is at the money and closes to marturity?”, consider the following, let’s use a call for example purposes:
Close to maturity, if you are in the money, you are likely to have the option pay-off, so any movement of the spot has a 1 to 1 effect on the price of the option, this means the delta is equal to 1 (i.e. if strike is 100, and spot is 102, and there is 30 seconds left to maturity, if spot move by 1 up or down, the effect on the option is the same, the payoff will increase/decrease by 1 with the change in spot). Now, if your spot is below the strike, the delta with little time left on the clock will approach 0 (i.e. if strike is 100, spot is 97, 30 seconds on the clock, the spot moving will have little effect on price of option, it’s likely to expire worthless, the payoff will go from nothing to nothing).
Now when you are at-the-money, you will have a very binary kind of effect where your delta will flip between 0 and 1 as the spot crosses back and forth across the strike. So for very very small change in spot (i.e. from 99.95 to 100.05), the delta will shoot from 0 to 1. This is why Gamma is so big, because Gamma is the change in delta (0 to 1) per change in spot (10 cents from 99.95 to 100.05).
 
It’s a calculus thing: gamma is the derivative of delta with respect to price of the underlying, so it’s the second derivative of the option price with respect to the price of the underlying.
What!?!
It’s how fast delta changes when the price of the underlying changes; think of gamma as a measure of how curved the price … well … curve is. The tighter the curve, the larger the gamma; the straighter the curve, the smaller the gamma.
When an option is close to expiration, the time value is close to zero, so the price curve is close to the payoff graph, which has a sharp corner at the strike price. Thus, the price curve has a very tight bend right near the strike price, and is nearly straight everywhere else; consequently, gamma is extremely large near the strike price, and close to zero everywhere else.
This is another case where drawing a picture will help immensely: the price curve when the option has a long time till expiry will curve gently over its entire length; the price curve when the option is very close to expiry will be essentially two straight lines with a sharp bend at the strike price.
 
vicky_cool400 wrote:Magic sir please help me in my FCFF q
Click to expand...
I’ll look at it in the morning; I’m still short on sleep from 15 hours Vancouver-to-Paris, 36 hours in Paris (teaching for 9 of them), and 15 hours Paris-to-Los Angeles.
 
S2000magician wrote:
vicky_cool400 wrote:Magic sir please help me in my FCFF q
Click to expand...
I’ll look at it in the morning; I’m still short on sleep from 15 hours Vancouver-to-Paris, 36 hours in Paris (teaching for 9 of them), and 15 hours Paris-to-Los Angeles.
Click to expand...
So you ARE a mere mortal? Makes me feel a little better.
I view you as the Spartan of CFA Charterholders and this forum.
 
Tks cleverCFA so much! Wish you the best for the exam. :)
 
rawraw wrote:
S2000magician wrote:
vicky_cool400 wrote:Magic sir please help me in my FCFF q
Click to expand...
I’ll look at it in the morning; I’m still short on sleep from 15 hours Vancouver-to-Paris, 36 hours in Paris (teaching for 9 of them), and 15 hours Paris-to-Los Angeles.
Click to expand...
So you ARE a mere mortal?
Click to expand...
I try not to be.
 
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