Option greeks

Option greeks

Throughout this site, market sensitivities will refer to the options mentioned in examples.

These sensitivities are often referred to as option greeks, they are a useful tool to a technical analysis, and truly represent an option’s inner working. We define them here:

Option’s Delta Δ:

Refers to the rate of change of value of the options contract, relative to the change of value of the underlying asset.

Equation: 

Mathematically it is the derivative of the contract price, with respect to the asset it represent’s value.

Delta will vary between 0 and +1.0 for a call option, and 0 to -1.0 for a put option.

Basically it’s a multiplicative factor to give you the amount the asset has changed for the amount your contract has changed.

Delta can also be used as an indicator of your probability of falling in the money, out the money, or at the money. The absolute value of delta is the probability you will fall in the money (with a profit). The exact calculation of that probability would be the dual delta, the first derivative of contract price relative to strike price.

Option’s Gamma Γ:

Refers to the rate of change of delta relative to a change in the underlying asset.

It is the second derivative of the price of the option, relative to that of the asset.

Equation: 

Its value is the amount that delta will change, for a change in the underlying asset’s price. For example if gamma is 0.05 and delta 0.5, then if the underlying asset’s price rises, the new delta will be 0.55, whereas if the asset’s price lowers, the new delta will be 0.45.

Gamma’s value is greatest at the money, and diminishes as you go further in the money or out of the money.

Option’s Theta Θ:

Theta measures the sensitivity of the option’s value to the passage of time, it represents the extent of time decay on the option.

Equation: 

Note that theta is non linear, rather it accelerates as the contract approaches expiry. It is always negative for holders, and positive for writers.

As it nears expiry it will reach it’s highest value.

Option’s Vega ν:

Vega measures the volatility of the contract relative to the volatility of the underlying asset.

Equation: 

Greater volatility implies greater prices for put and call options contracts, because you have more chance of falling in the money.

 

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