Estimating Option Prices After a Stock Move With Greeks
Several methods can be used to estimate the price of an option after a move in the price of the underlying stock.
The most widely used method involves utilizing the "Greeks" to calculate the option price.
The "Greeks" Mathematical equations have been developed to help estimate how much an option premium will change as the underlying stock moves and time approaches expiration.
These equations are commonly referred to as the "Greeks' and they include, Delta, Gamma, Vega and Theta.
The following is a brief explanation of how they are used to estimate the change in option pricing.
Delta is a measurement that estimates how much an option premium will increase or decrease with every dollar movement in the underlying stock or index.
An at-the-money option typically has a delta of approximately +/-.
50 (+.
50 for a call and -.
50 for a put).
This means, for the next dollar movement in the stock, the option price will move approximately 50 cents.
As a stock moves up, the delta of a call option increases in value, and decreases as the stock moves down.
The delta of a put option de-creases as a stock moves up and increases as the stock moves down.
The maximum delta an option can typically have is 1.
0.
This can happen when an option is in-the-money and approaches expiration, that is, trading at parity.
Gamma is a measurement that estimates the rate of change in an option's delta for each dollar move in the underlying stock or index.
Because stocks have different volatilities (measured by Vega), the gamma of a stock's options will vary from one stock to another.
A more volatile stock will usually have a lower gamma.
Therefore, the more volatile the stock, the less its options deltas will either increase or decrease with each dollar move.
This is because a move is more significant on a stable stock than one that is more volatile.
For example, a stable stock priced at 50 may see its 50 strike call increase in price from $2 to $2.
50 when the stock moves to 51 and increase to $3.
20 when it goes to 52.
The delta for the first dollar move was.
50, increasing the option price fifty cents.
The delta increased to.
70 with the option price increasing by seventy cents when the stock moved to 52.
The option's gamma was therefore.
20 as the delta increased from.
50 to.
70.
However, the more volatile stock trading at 50 may see its 50 strike call increase from $4 to $4.
50 when the stock moves to 51 and then to $5.
05 when it moves to 52.
The delta for the first dollar move was.
50 and the option premium increased by fifty cents.
When the stock moved to 52 the option premium increased by fifty five cents giving it a delta of.
55.
The option's gamma was therefore.
05.
With a stock move from 51 to 52, the delta value of the volatile stock's option moved from.
50 to only.
55 when the stock went from 51 to 52, while the more stable stock's delta moved from.
50 to.
70 when the stock priced moved from 51 to 52.
In addition, the delta and gamma values will change as an option moves closer to expiration.
This rate of change is estimated by measurement referred to as "Theta.
"
The most widely used method involves utilizing the "Greeks" to calculate the option price.
The "Greeks" Mathematical equations have been developed to help estimate how much an option premium will change as the underlying stock moves and time approaches expiration.
These equations are commonly referred to as the "Greeks' and they include, Delta, Gamma, Vega and Theta.
The following is a brief explanation of how they are used to estimate the change in option pricing.
Delta is a measurement that estimates how much an option premium will increase or decrease with every dollar movement in the underlying stock or index.
An at-the-money option typically has a delta of approximately +/-.
50 (+.
50 for a call and -.
50 for a put).
This means, for the next dollar movement in the stock, the option price will move approximately 50 cents.
As a stock moves up, the delta of a call option increases in value, and decreases as the stock moves down.
The delta of a put option de-creases as a stock moves up and increases as the stock moves down.
The maximum delta an option can typically have is 1.
0.
This can happen when an option is in-the-money and approaches expiration, that is, trading at parity.
Gamma is a measurement that estimates the rate of change in an option's delta for each dollar move in the underlying stock or index.
Because stocks have different volatilities (measured by Vega), the gamma of a stock's options will vary from one stock to another.
A more volatile stock will usually have a lower gamma.
Therefore, the more volatile the stock, the less its options deltas will either increase or decrease with each dollar move.
This is because a move is more significant on a stable stock than one that is more volatile.
For example, a stable stock priced at 50 may see its 50 strike call increase in price from $2 to $2.
50 when the stock moves to 51 and increase to $3.
20 when it goes to 52.
The delta for the first dollar move was.
50, increasing the option price fifty cents.
The delta increased to.
70 with the option price increasing by seventy cents when the stock moved to 52.
The option's gamma was therefore.
20 as the delta increased from.
50 to.
70.
However, the more volatile stock trading at 50 may see its 50 strike call increase from $4 to $4.
50 when the stock moves to 51 and then to $5.
05 when it moves to 52.
The delta for the first dollar move was.
50 and the option premium increased by fifty cents.
When the stock moved to 52 the option premium increased by fifty five cents giving it a delta of.
55.
The option's gamma was therefore.
05.
With a stock move from 51 to 52, the delta value of the volatile stock's option moved from.
50 to only.
55 when the stock went from 51 to 52, while the more stable stock's delta moved from.
50 to.
70 when the stock priced moved from 51 to 52.
In addition, the delta and gamma values will change as an option moves closer to expiration.
This rate of change is estimated by measurement referred to as "Theta.
"
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