I keep getting delta and gamma mixed up on the mocks. Can someone provide a succinct description of how they are different and how they respond to changes in the underlying stock, as well as the effect if the option is close to the money or deep out of the money? Thanks!
Delta = change in OPTION price / change in UNDERLYING price Gamma = change in DELTA / change in UNDERLYING price Its a second order estimation. Equivalent to convexity. Gamma is high when underlying price is at the money ==> more convexity ==> simple linear Delta relation invalid ==> Delta is poor estimate for change in option price when underlying price is at the money
Gamma is just the rate of change of Delta. As janard mentioned Gamma is highest when an option is at the money. Gamma is highest for a call option when the Delta equals 0.5 Gamma is highest for a put option when the Delta equals -0.5 When options are way out of the money and deep in the money gamma will be very low.
Chuckrox8 Wrote: ------------------------------------------------------- > Gamma is just the rate of change of Delta. As > janard mentioned Gamma is highest when an option > is at the money. > > Gamma is highest for a call option when the Delta > equals 0.5 > Gamma is highest for a put option when the Delta > equals -0.5 > > When options are way out of the money and deep in > the money gamma will be very low. How did you arrive at this 0.5/-0.5 relation? I don’t seem to have seen it anywhere.
Yeah, I disagree with that statement… I was waiting for somebody to confirm it because I’ve never heard of that relationship before.
Just as delta changes, so does gamma. If you were to look at a graph of gamma versus the strike prices of the options, it would look like a hill, the top of which is very near the ATM strike. Gamma is highest for ATM options, and is progressively lower as options are ITM and OTM. This means that the delta of ATM options changes the most when the stock price moves up or down. ATM equals “At The Money”. ATM Delta for a call option is +0.50.
That’s not true ^^ regarding the 0.5. Everything else is right.
yeah, 0.5 theory is wrong. Even outside the curriculum in John C Hull’s Derivatives books this is stated nowhere… prove me wrong if you want, but I have no idea where you’re drawing this conclusion…it’s not from the books, that’s for sure…
I agree with you guys on the 0.5 value of Delta. I was wrong to say that it is “equal”. The Delta of an ATM call is “around” 0.5. Just pull up an option chain for any stock trading right at a strike price. i.e. Home Depot Currently trading @ $35.05 The delta of the call option contracts is 0.52 I think it’s safe to say that the delta for an ATM call option will be between .45 and .55.
Delta for call option in the money 1 Delta for call option out of money 0 Delta for put option out of money 0 Delta for put option in the money -1 Gamma is highest when it is at the money.
Gamma is large for options that are at the money (i.e. very sensitive to changes in the underlying stock price), and small for options that are far out of the money. If gamma is large, delta hedging doesn’t work as well because you have to continually adjust. (This theory is garbage anyway, because you have to constantly adjust either way, but just go with it.)
No… We just haven’t learned the whole process from this curriculum… Wait until (level 3 maybe?) … There is Delta, Gamma, Vega hedging… Let’s just say level 2 derivatives are very simplified versus grad school or more in depth courses on this material…