The Greeks are mathematical methods of measuring and valuing options, Delta and Theta are two every trader should be familiar with. If you are a directional trader the Greeks can mean the difference between profit and loss. More advanced traders can use these two numbers to set up delta-neutral positions that produce profits regardless of the movement of the underlying asset. In either case the importance of these two numbers can not be understated. To help put it into perspective let me ask you this, have you ever had an option trade where the underlying asset moved in the proper direction, closed in the money and still lost you money? I bet if we were to examine delta and theta we would find the reason why.

Option Delta

Option delta is a measure of the amount of change the price of an option will have relative to the change in price of the underlying asset. The delta is expressed as number between 0.00 and 1.00. When buying calls, a delta of 0.50 means you can expect the value of the option to rise by \$0.50 for every dollar of movement in the underlying asset. A delta of 0.60 could expect to see a gain of \$0.60 for every dollar of gain in the underlying. Delta for put options is expressed as a negative because as the price of the underlying rises the option loses value, when the price of the underlying falls the value of the option rises.

Options that are in the money have a higher delta, options that are out of the money have a lower delta and options that are at the money tend to have a delta near 0.50. The great news about delta, for directional traders at least, is that as the price of the underlying asset moves deeper into the money delta goes up. This means that as asset prices move higher the change in delta and the change in option prices relative to each dollar of movement in the underlying goes up. Delta also tends to go up as an option approaches expiration.

There is a difference in delta when considering long or short options. For example, a long call has a positive delta but a short call has a negative delta. Short calls have negative delta because as the price of the underlying moves higher and the options gains in value, the position loses value for the seller. In the case of puts a long position has a negative delta and a short position has a positive delta, due to the inverse relationship with prices. The difference in positive and negative delta is the basis for more complex positions and leads to the term position delta.

Position delta is the sum of the deltas of options purchased or sold on the same underlying. A simple straddle, buying a long call and a long put at the same strike with the same expiration date, tends to have a delta of 0 because as one position gains value the other loses it. This type of position is used when a sharp move in price is expected, in either direction, or in times of high volatility where it may be possible to profit from both positions.

Option Theta

Option theta is the measure of an options time decay, it is an expression of the amount of value an options will lose as it approaches expiration. Theta is subject to volatility, the amount of time until expiration and the price of the underlying in relation to the strike price. Theta, unlike delta, is always negative for long positions because an option is always losing time value up to and until expiration day. At that time there is no time value left, only intrinsic value, if there is any to be had. It is expressed as a dollar amount and can be quite high depending on the value of the option and the underlying asset. A theta of 0.25 means the option will lose \$0.25 per day, but this value is not constant.

The more time until expiration the more time value an option will have and the less effect of theta, however, as the option approaches expiry theta goes up. Volatility can also have a great impact on theta. As volatility goes up so too will theta because as volatility rises, so does the premium you pay in order to own the option. More time value, premium, equals higher theta. Yet another factor affecting theta is the price of the underlying in relation to the strike price. The deeper in the money an option is the lower the theta because the price of the option is based more on intrinsic value than time value. An out of the money option close to expiry will have the highest theta.

This table gives an example of how theta affects options that are at the money, out of the money and in the money in relation to expiration day. In the money options have the lowest theta, out of the money have the highest and they all show marked increases in theta as expiration draws closer. The time period in which there is the greatest amount of time decay, and greatest increase in theta, is the final month before expiry. This is one reason why front month options are ideal for sellers.

Now let's think about theta in terms of strike and expiry month. Two options with the same strike and different expiry months, assuming they both have at least 2 months until expiry, can have similar theta values up to and until the final month before expiration. The price of each will be different, the one with more time will cost more, but in terms of time decay theta will be nearly the same, this next chart illustrates the concept.

A short option has a positive theta, this is because as the option loses time value its value decreases and the seller profits. This fact is the basis for many types of advanced options strategies and is used in combination with delta. A delta neutral position can be created in which the long portion of the position has a lower theta than the short position creating a price differential favorable to the trader.

Delta And Theta For Directional Trading

Delta and Theta are very important for directional traders for two reasons; strike price and expiry month. When it comes to choosing an option it can be attractive to buy out of the money (low delta) and front month (high theta) because those options are cheaper relative to other options, and the amount of profit to be made if it moves into the money is much greater. The risk is that the option won't move enough to create a profit or won't move enough to for profits to overcome time decay. It makes no sense to buy a low delta option when the expected move is relatively small, and/or when theta is so high as to wipe out any gains.

What is comes down to is how much movement is expected in the underlying asset and how soon the move is expected. Personally, I prefer to buy at the money or slightly in the money options in order to get a delta of at least 0.50, and to choose an expiry not the front month. That way I can capture at least half of any move that does occur, cut down on the risk of time decay and ensure enough time for the expected move to occur. Sometimes this means spending more on the option than strictly necessary but is worth it in order to reduce time risk and to ensure profitability. The trick is to find the right balance between the amount of expected movement in the underlying, when the move is expected to occur, the impact of delta and the affect of time decay.