# Gamma and Delta

Gamma is largest when it is at the money and close to expiration. How about Delta? I would says Call delta is largest when in the money, since it’s closer to 1. Put delta is largest when out of money since closer to 0 relative to -1. I’m not sure about the put delta, anybody confirm?

have a look over here… if you understand these graphs you are good. http://cdmurray80.googlepages.com/optiongreeks

thanks barth, not sure if I understand the graphs correctly. seems like both call and put delta largest when in the money? For put delta, the graph peaks at -1, which is when put delta is in the money. can you explain?

Put delta is largest when it is negative one…the negative is a directional sign, i.e., puts go up in value when underlying goes down. So an in the money put will have a delta of closer to -1 than 0, and an ITM call will have a delta closer to 1 than 0. If you think about delta in terms of its being a hedge ratio, the more option is in the money, the more stock you need to hedge against its movement. REgarding gamma, it is largest when right at the money with little time to go…think about when the option is expiring, strike is 50 and the stock is 50…the delta is .5 on a call but at the end of the day will be 1 if the stock is 50.01 and 0 if the stock is 49.99…thats some seriously big gamma…no go back to a year from expiration, same scenerio…the delta of a 50 call with stock at 50 won’t change very much if the stock moves up or down a buck lets say…gamma much smaller. simplistic explanation but hope it helps.

before you look at them in 3-d look at them in 2-d, based on changes in price. call: delta goes to 1 as the stock price increases or option is in the money. put : delta goes to minus 1 as the stock price decreases or option is in the money. depending on how you define largest, you find the ans above. why is the put delta -1 when option deep in the money… assume exercise price X=100, stock trades at 10 - what happens? the probability of the option expiring deep in the money is big. the stock would have to increase 900% for it to expire out of the money. the intrinsic value of option is high. the option resembles your stock and a hedge would make sense since the gamma of a deep in the money option goes to 0. such an option would prob trade around 93 - 95 depeding on time factor, RFR, etc… a thing that is traded on eurex are LEPO’s. low exercise princing options. same thing: x=low & stock price is 100. the option has a delta of 1 (assume call). hope this helps a little.

Thanks guys. I think largest means the absolute value of the delta. so I think I can conclude the following: Gamma is largest when at the money and closer to expiration BOTH put and call delta largest when IN the money.

yes. correct… if defined in absolute terms.

BUT…make sure you watch for this…if the question asks whether the delta of a put gets larger or smaller when the stock goes down, the correct answer is smaller because it gets more negative and vice versa…i got this type of question wrong on one of the tests (cfai, schweser?)…have traded options for 20 years and think in absolutes instead of like a CFA level 2 candidate…wont get fooled again.

petetini Wrote: ------------------------------------------------------- > If you think about delta in terms of its being a > hedge ratio, the more option is in the money, the > more stock you need to hedge against its > movement. > hmmm i think this is incorrect… the more option is in the money, which means delta would already be 1, then the number of shares needed to be hedged would be exactly the same because the delta is 1. if delta is 0.01 then the number of option needed to hedge is higher. why? hedge ratio: 1/0.01 = 100

sorry, i am confusing you because i am talking from the perspective of hedging the option, not hedging the stock…i am an options trader…so, if you own 1 call and its in the money, the hedge is sell 100 shares, if you own an at the money call with a 50 delta then the hedge is sell 50 shares. like i said above, i have a tendency to think like an options trader not a CFA candidate. But you are absolutely right from the perspective of hedging stock, if the delta is .5 then you need 2 options per 1 share 1/.5. sorry for confusion.

petetini Wrote: ------------------------------------------------------- > BUT…make sure you watch for this…if the > question asks whether the delta of a put gets > larger or smaller when the stock goes down, the > correct answer is smaller because it gets more > negative and vice versa…i got this type of > question wrong on one of the tests (cfai, > schweser?)…have traded options for 20 years and > think in absolutes instead of like a CFA level 2 > candidate…wont get fooled again. thanks. when stock price goes down, S < X, it’s in the money put, it’s closer to -1, so put delta gets smaller when in the money, or conversely, put delta is larger when out of the money? i.e., my conclusion in the first post is correct?