Delta:

The delta is a measure of how an option's value changes with respect to a change in the price of the underlying contract. The delta is slower than underlying price change and the delta must be 0 to 1 for long call or short put, 0 to -1 for short call or long put. If the option is far out of the money, the delta is close to 0. If the delta is close to 1 for call, -1 for put, the option is deeply in the money. For example, if the delta is 0.25 and underlying price rises 1, the option can be expected to rise 0.25 (1 x 0.25). if the delta is 0.75 and the underlying price raises 70, the option premium can be expected to gain 62.5 (70 x 0.75).

For hedge ration calculation, the underlying delta is always 1, so a 5 long call option with 0.4 requires 2 short underlying contracts (5 x 0.4 = 2).

Also other characteristic of the delta is that; if we can ignore the sign of the delta, we can use the delta as approximate probability that option will be finish in the money. The dual delta is the actual probability of the option being finish in the money.

Gamma:

The gamma is the amount of the delta changes as compared to a 1 point increase in the price of underlying contract. For example, the gamma 0.05 means it will increase 0.05 delta when the underlying increases 1 point. The gamma becomes important when the option approaches to its maturity date because gamma is more sensitive than the delta.

Theta:

The theta is the value of how quickly loosing time value for the option premium. The theta is always expressed as a negative value because the option value will be reduced based on the time of passage. This is the rough estimation of theta only in the case of at-the-money that 40 days option's theta is two times of 160 days option's theta. The approximate calculation is that [square root(160/40) = 2]. Also the relative size of the gamma and theta will correlate. A large positive gamma move related with a large positive theta. As mentioned above, the at-the-money gamma becomes increasingly large. This is the same also for the theta.

Also the other aspect of time value, the option value can be consist of two parts, instinct value and time value. The instinct value is the value that the option is executed immediately with strike price. For example, the strike price is $50 and the price of option is $60, then the $10 is instinct value. The intrinsic value for call is underlying price – strike price whereas intrinsic value for put is strike price – underlying price.

The time value is the value which is exceeded from intrinsic value. For example, the premium is $8, the strike price is $5, and the underlying price is $7, then the intrinsic value will be $2 and the time value will be $1.

Vega (Kappa):

The vega is given in point change in theoretical value for each one percentage point change in volatility. If an option of the vega is 0.1 and 20% volatility of the option price is $20, the 21% volatility of the option price will be $20.1 and the 19% volatility of the option price will be $19.9.

The vega of the shorter option is more sensitive than the vega of the longer option. Time and volatility are closely interconnected.

Rho:

The rho is the sensitivity of an option's theoretical value to a change in interest rates.

Delta Neutral Hedge:

Gamma Neutral Hedge:

The Gamma Neutral Hedge is that trading option position The total gamma value of the position is zero or near zero.

References:

Options for the beginner and beyond by W. Edward Olmstead

Futures and options markets by Colin A. Carter

Option volatility & Pricing by Natenberg