Understanding The Greeks

by Adam Beaty

Delta:  The measure of how much exposure your option position has to the underlying is Delta.  Delta lets you know how much your option position will change for a 1-point move in the underlying.  Call deltas range from 0.0 to 1.0 and Put deltas range from 0.0 to -1.0.  The underlying always has a delta of 1.

For example:

Delta of a call: .60

Price of call: $1.00

Price of underlying: $52.00

If the underlying increases to $53.00 your option is now worth $1.60.

If the underlying decreases to $51.00 your option is now worth $0.40

The further out of the money the option the lower the delta.  Deep out of the money options have deltas closer to 0.0 (for calls and puts).  Deep in the money options will have a delta closer to 1.0 (for calls) or -1.0 (for puts).  We can use this same logic to apply probability to our position.  You can use delta to give you a rough estimate of probability for an option finishing in the money.  So in our example above, our calls has a 60% (.60 delta) of finishing in the money.

You can always find the strike that is at the money by looking for the delta closest to .50.

Deltas are not constant as they will move over the life of the option as time, price, and volatility change.

If you are trading a position comprised of more than one option than you can total up the deltas to figure out the total delta for the position.

Position Delta = Delta x Shares per Contract x # of Contracts

 For example:

From here we can see the position is delta long 330.  This is equivalent of owning 330 shares of the underlying stock.  If the delta was around 0.0 we would call it delta neutral.  Delta short is a negative overall delta.

 From this example we can also see that Long Calls and Short Puts have a positive delta (they both benefit from an increase in the underlying).  Short Calls and Long Puts both have negative deltas (they both benefit from a decrease in the underlying).

Gamma: To figure out how fast the delta is going to move we look at Gamma.  Earlier we talked about how delta is not a consistent number and how it will change over the life of an option.  Gamma gives us the tool to measure that change.  Again, we can think of the change in terms of a 1-point move in the underlying.

For example:

Delta of call: .60

Gamma of call: .05

Underlying: $46.00

If the underlying increases to $47.00 then the delta will now be .65.

If the underlying decreases to $45.00 then the delta will be .55.

Like delta, gamma will also change over the life of the option.  This is because a delta cannot go beyond 1.0 or -1.0.  A gamma must change to slow down the movement of delta.  The gamma of at the money options will be the highest.  Deep in the money and deep out of the money options will have the smallest gamma.

Gammas are always expressed as positive numbers, and will increase dramatically near expiration.  This factor is what makes the Weekly options desirable.  Even a small move so close to expiration can change the option price greatly.

Like delta gamma can be calculated for an entire position consisting of more than one option.  We will use our previous example on delta.

As you can see this position is positive gamma at +10.  So if the underlying moves up by 1-point our new delta will be +340 (330 + 10).  If the underlying moves down 1-point our new delta will be +320 (330 – 10).  We also notice that the underlying has a gamma of 0.0.  The underlying has a 1.0 delta and thus cannot change so we get a 0.0 gamma.  We also notice Long Calls and Long Puts have positive gammas and Short Calls and Short Puts have negative gammas.

Later we will show you how to make your position both delta and gamma neutral.  As we will discover it is not enough to be delta neutral as that only last until the underlying moves.

Theta: The measure of time decay comes from theta.  One thing all option traders need to be aware of is an option’s time decay.  Time decay is the enemy of the option buyer and friend of the option seller.  Theta is expressed as a negative number of cents of decay for each day.  So a theta of -.06 means the option price will drop 6cents each day if everything else remains the same.

Time decay is not linear and will increase rapidly when the option nears expiration.  Also near expiration most brokerages, option chains, and models will report theta that is not accurate.  The majority of the time thetas near expiration that will report a number that will take the option price below 0 before expiration.

Unlike delta, gamma, and vega time decay cannot be hedged against so it is usually not of major concern to overall positions.  Understanding that it is there and how it will affect your positions is more important.  However, you can figure out the overall theta of position that has more than one option.

Position Theta = Option Theta x Shares per Contract x # of Contracts

Vega/Tau/Kappa:  Volatility always gets a wide variety of names because Vega is not actually a Greek letter, so in some cases you will see it referred to as Tau or Kappa.  In our case we will also refer to it as Vega since that is the generally accepted name.  Vega measures the change in option price according to the change in volatility.  Volatility is always the X-Factor in options pricing.  That is because it is always a guess, always misunderstood, and usually not taken into major account.  Unlike all other inputs into an option pricing model, volatility is the only one that is not a concrete number.  With that being said, volatility is the most important factor in options.

A high volatility means higher option prices.  This is because people expect the underlying to move more so therefor option prices are higher to reflect that.  That means if volatility goes up your option price will rise.  That means if volatility goes down, your option price will go down.  This may seem like an elementary concept; however most beginner option traders will ask the question, “Why did my stock go in the right direction, but my option lose money”.

Learning volatility and how it moves and affects options will put you way ahead of the pack when you being option trading.

Rho: This is the poor forgotten Greek.  Rho tracks interest rates and how they affect option prices.  With an increase of interest rates we have an increase in call prices and a decrease in put prices.  When interest rates decrease we see a rise in put prices and a decrease in call prices.  Rho measures this movement.

LEARN MORE ABOUT OPTIONS by checking out Adam's Optionology Section on SharePlanner.