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Effects of a stock split on Delta-Gamma-Vega-Theta?
- Thread starter AMW
- Start date
Quote from AMW:
On a stock split, what happens to the position's DGVT?
I think-
Delta get cuts in half.
Gamma is squared.
Gamma is the first derivative of delta, so if delta gets cut in half gamma gets cut in half too.
Also, the delta of "the position" (your option holding) actually [/i]doubles[/i], because you will have options on twice as many shares (at half the strike). Which means that gamma doubles with it. Of course, the split also cuts the stock's price movement in half, so it's a wash. As it should be.
Right on the delta(same as a stock position....if a stock split).
What your saying makes sense but I still feel that The gamma is either squared or the square root is taken. Thank you for the response. I'll try and do some research at some point today. Others please feel free to chime in..........
What your saying makes sense but I still feel that The gamma is either squared or the square root is taken. Thank you for the response. I'll try and do some research at some point today. Others please feel free to chime in..........
Quote from AMW:
To figure out gamma. You square the the factor of the split and multiply.
2 for 1=Gamma x4.
3 for 1=Gamma x9
Unpossible.
1) Gamma is the (calculus kind of) derivative of delta. That means if delta is multiplied by a number, gamma is multiplied by the same number and nothing else changes.
1A) Gamma is how much delta changes with price. That means the difference between deltas at different strike prices is the sum (integral) of all the little gammas along the way. If gamma got multiplied by 9, the difference in delta between two strikes would also get multiplied by 9, and you can quickly see how that would get ridiculous.
2) In general, if a stock does nothing but split and your gamma suddenly gets multiplied by 9, that should immediately strike you as wrong. Stock splits don't change anything fundamental about your position.
Here's the only proof I could find online. This guy writes for minyanville.com.
"So what happens to the options when a stock splits? Well, on a 2:1 split, your delta obviously doubles, same way a straight stock long doubles in quantity.
Your gamma actually quadruples though. Why? Well, think about it. Gamma (as is pertains to your position) is the amount your delta changes per 1 point move in the underlying stock. So if you split the stock, the gamma should double too, right?
Wrong. That *new* gamma now measures the change in your delta per half-point move in the stock, so you have to double it AGAIN to get your new gamma back to it's true definition.
Got all that? Don't worry, you won't be tested. And rest assured it won't effect your actual risk/reward picture; it is exactly the same pre and post split, it just looks different.
All that was above was my attempt at a layman's explanation for what happens to gamma. The real *formula* is that you square the factor of the split. In other words, in a 3:1 split, your gamma goes up by a factor of nine, in a 4:1 split it goes up by a factor of 16, and so on. But the most important thing to remember is that RISK/REWARD IS UNAFFECTED."
"So what happens to the options when a stock splits? Well, on a 2:1 split, your delta obviously doubles, same way a straight stock long doubles in quantity.
Your gamma actually quadruples though. Why? Well, think about it. Gamma (as is pertains to your position) is the amount your delta changes per 1 point move in the underlying stock. So if you split the stock, the gamma should double too, right?
Wrong. That *new* gamma now measures the change in your delta per half-point move in the stock, so you have to double it AGAIN to get your new gamma back to it's true definition.
Got all that? Don't worry, you won't be tested. And rest assured it won't effect your actual risk/reward picture; it is exactly the same pre and post split, it just looks different.
All that was above was my attempt at a layman's explanation for what happens to gamma. The real *formula* is that you square the factor of the split. In other words, in a 3:1 split, your gamma goes up by a factor of nine, in a 4:1 split it goes up by a factor of 16, and so on. But the most important thing to remember is that RISK/REWARD IS UNAFFECTED."
Quote from AMW:
Wrong. That *new* gamma now measures the change in your delta per half-point move in the stock, so you have to double it AGAIN to get your new gamma back to it's true definition.
That "wrong" is wrong. It double-counts the effect of the split. He's counting a factor of 2 because delta changes, and another factor of 2 for the split. Problem is, the "because delta changes" *is* the split.
Gamma is the "slope" of delta. If you quadruple the gammas, some of the deltas will more than double, and some of the deltas will be greater than one.
Also, how can the risk/reward be unaffected if gamma changes so drastically? Gamma is a big part of risk/reward because, again, it tells you how quickly delta changes.
Rather than arguing the maths, I opened up a pricing model and simulated a 2 for 1 stock split and here're the results.
On a position basis:
Delta doubles.
Gamma quadruples.
Theta, Vega and Rho stay the same.
On a per option basis:
Delta stays the same.
Gamma doubles.
Theta, Vega and Rho halve.
(However, since your number of contracts doubles you need to multiply the greeks by 2 to get position greeks, which corresponds to the above results)
On a position basis:
Delta doubles.
Gamma quadruples.
Theta, Vega and Rho stay the same.
On a per option basis:
Delta stays the same.
Gamma doubles.
Theta, Vega and Rho halve.
(However, since your number of contracts doubles you need to multiply the greeks by 2 to get position greeks, which corresponds to the above results)