Hello,I am using BS methodology to value a USDTRY plain vanilla european call option. It's delta 0.52 and gamma 3.14Here are the inputs that I use :Spot : 1.8223Strike : 1.861 R(Foreign) = %0.34R(Domestic) = %8.48Volatility = %13.9Time to maturity(years) : 0.25My question is, as this is an option which's delta range 0 and +1, how come gamma(which suppose to show change in delta as underlying changes 1 unit) can be more than 3? How should I interpret this gamma value? Should I make some transformation to gamma? I have looked anywhere but could not find an answer. This maybe the easiest problem that is asked ever but if you help me I will appriciate.Thanks in advance

Delta is what's called a first derivative (in the calculus sense) and Gamma is a second derivative.Gamma is also the first derivative of Delta. [more carefully, the first S-derivative]Just because a function is bounded (Delta) doesn't mean its first derivative is bounded.In fact, Gamma can be arbitrarily large.The reason is that, at expiration, Delta switches from 0 to 1 as a step function at the strike: S=K.This makes its S-derivative (Gamma), in fact, *infinite* at S=K.Reflecting this infinity, close to expiration and close to S=K, Gamma becomes very large.p.s. The discussion of "derivative" at wikipedia is good and briefly mentions the step function ...Beyond that, pick up a calculus text.

Hi Alan,Thank you very much for your reply, when I think of delta function, it is totaly understandable that gamma can be infinite at S=K, and close to zero for deep in or out of the money. But my real problem is, I can not understand the meaning of this gamma values in practice. Let me explain it this way, Lets say my option is 1000000 USD(call), 1861000 TRY(put). If delta is 0.52 than I know that I should sell 520000 USD in order to have delta neutral position. But lets say I would also like to make gamma hedging. This is where I can not move one step further. So if you can help me in fillling the blanks of the sentences below, I hope everything will be ok for me :As gamma is 3.14, if the underlying price moves from ...... to ......, then option delta will move from ....... to ......... .In order to have delta-gamma neutral portfolio we should ...... Thanks in advance

QuoteOriginally posted by: kremerAs gamma is 3.14, if the underlying price moves from 1.8223 to 1.8224, then option delta will move from 0.52 to 0.520314. In order to have delta-gamma neutral portfolio we should buy/sell a 2nd option with a gamma of 3.14 (weighting the two hedges to stay overall delta & gamma neutral), and (perhaps) rebalance as necessary sorry for all the edits.HTHp.s. For more discussion, try the search function with "Delta Gamma" in the title.

Thank you very much. It is very clear now. In general I may say that, if gamma is 3.14 and if I change undelying 1 bp than delta will effect (3.14 * 0.0001), similarly if lets say gamma is 0.1 and if I change underlying 1(100 to 101 eg.) than delta will effect (0.1 * 1)?Best regards...

Approximately. It strictly holds only in the infinitesimal limit. If you are close to expiration, close to at-the-moneyand so Gamma is very large, the approximation will become very poor.