The Greeks


Basic Terminology  Options Volatility Greeks
Long/Short Stock Strategies Calendar Spreads Straddles and Strangles Vertical Spreads

Greeks
     Delta
     Gamma
     Theta
     Vega
     Rho
Dividends
Interest 

The Greeks

The Greeks help us determine how a number of factors affect the price of an option. Many of the questions we get on the site regard trade management; being aware of greeks will help with position management. They are also very important for considering overall portfolio risk and considering your portfolio versus overall market conditions.

Delta
Delta is a forecast of how a directional change in the underlying will affect the price of an option – a measure of directional risk. A +50 delta option will go up $.50 with a +$1 change in the underlying. A -50 delta option will go down $.50 with a +$1 change in the underlying. Calls have positive delta and puts negative. An in-the-money option will have a delta larger than 50 and an out-of-the-money option will have a delta smaller than 50. The delta changes as the underlying changes, so a 50 delta call may become an 80 delta call (up to 100) as stock goes up or a 20 delta call (down to 0) as stock goes down. The delta of an option also changes with implied volatility changes and with time. (As implied volatility gets higher all options get closer to +/- 50 deltas as any outcome becomes equally possible.) Therefore position deltas are always changing.

Delta can be thought of a couple ways. On an individual option the delta represents the probability that the option will expire in the money. A positive or negative 10 delta option has a 10% chance of finishing in the money. This can be helpful in considering which options to buy or sell. The second way is to consider that an underlying contract has a delta of 100. So the overall position deltas will tell you what your risk is in terms of a directional move in the underlying. If you are long 500 deltas this is like being long 5 shares of stock. You might be long 500 deltas by being long calls or short puts (negative times negative equals positive). So when considering your overall position conviction this can be helpful. You then ask yourself, “Am I so sure of the direction of this underlying that I would be willing to be long 5 contracts?”

Deltas help with trade and portfolio management. When you put on a particular position in the options of an underlying, that position will have an overall delta. Maybe you are long 10 50 delta puts (-500 deltas) and short 10 25 delta puts (+250 deltas). Your total position delta is -250 deltas. With this position you are betting that stock will go down. As stock moves this position delta will change. Thus you can make a decision whether to adjust your position, maybe rolling out of one strike line into another, taking off a position, or hedging with stock. It is important to be aware of how the deltas are changing to make sure your position is still reflecting your opinion and conviction and has not become too risky.

You might also keep in mind overall portfolio deltas in respect to the market in general. Perhaps you have a broad portfolio of positions and find that you are long many deltas overall. This means your risk is to the downside. Say the market is at its highs for the year. If you feel the market will continue to rise, then your overall portfolio position reflects this opinion. If you feel this is a top then you may want to make some changes to your portfolio.

Gamma
Gamma is the rate of change of an option’s delta as the underlying moves. This may seem one too many removes from reality, but gamma is actually quite important as a risk measure. Gamma is greatest for at-the-money, front month options and gets larger closer to expiration. It is positive for calls and puts so if you buy an option you get positive gamma and sell an option you have negative. Gamma goes down in both directions as you get away from at-the-money.

Gamma is a measure of movement risk. I think of gamma as my margin of error. Small gamma positive or negative, I might be ok if the poop hits the fan; large positive gamma and I need the poop to hit the fan (so I don’t die slowly of decay); large negative gamma and I need to turn in my badge and gun and take the kids out of private school if the poop hits the fan. So you only want to be short a lot of gamma if for some reason you are fairly sure that the poop won’t hit the fan between now and when your gamma expires, thus not in a Chinese potential fraud stock and probably not in a biotech. Again, on this site we will generally be discussing trades where we are flat to long options and therefore mostly positive gamma or small negative.

One way to think of gamma is in terms of imagining movement. If you have a positive gamma position, then as the underlying moves up you get longer deltas, a good thing, and as it moves down you get shorter deltas, also a good thing. So if you are actively managing your position with stock hedges you can sell stock when it goes up and buy stock when it goes down to stay delta neutral. Thus if stock moves around a lot you are scalping stock and making money. You want it to move. In a negative gamma position, when stock goes up you are getting shorter deltas, a bad thing, and when stock goes down you are getting longer deltas. So the stock movement is going against you both ways. Again if you are hedging with stock you would need to buy stock on the way up and sell it on the way down, reverse scalping for losses. Thus, you want stock to stay still.

In managing risk in a position, you add gamma to the delta in a positive stock move and subtract in a negative move to figure out what the delta will be (often good to look up or down 10, 20 and 40 percent for risk measure.) If you are long 300 deltas and long 200 gamma then if stock goes up $2 you will be long 700 deltas (300 + (200×2)) and if stock goes down $2 you will be short 100 deltas (300- (200×2)). If you are short 200 gamma then if stock goes up $2 you will be short 100 deltas (300 + (-200×2)) and if stock goes down $2 you will be long 700 deltas (300 – (-200×2)). You want to keep your gamma position in mind especially if you are keeping track of your delta risk limits. Say your delta is -500 and that is a number you are comfortable with. If your gamma is -200 then a $2 gap up in the stock with give you a delta of -900, which you may feel differently about. So you always want to be aware of how your delta position will change with stock gaps, which can be done by keeping your gamma in mind.

Theta

Theta is the amount of money an option loses in a day. It is negative because options lose money as time passes. Theta is greatest for at-the-money options and gets larger the closer the option gets to expiration. Theta is the other side of the coin of gamma. A large positive gamma position will correspond with a large negative theta position. Your theta position tells you how much money you will lose or make every day if everything stays status quo. So traders don’t like to see a big negative theta position going into a weekend, especially a long weekend.

Sheldon Natenburg has a good quote in his book Option Volatility and Pricing:

Every option position is a tradeoff between market movement and time decay. If price movement in the underlying contract will help a trader (positive gamma), the passage of time will hurt (negative theta). And vice versa. The trader can’t have it both ways. Either he wants the market to move or he wants it to sit still. p. 111

Delta, gamma and theta tell us what our position wants the underlying to do and what will happen if it doesn’t. We want to make sure that this corresponds with our opinion, our conviction, and our risk tolerance.

Vega
Vega measures the change in an option’s price for a one point move in implied volatility. An at-the-money option will have the highest vega, but an out-of-the-money is most affected on a percentage basis by a change in volatility. Vega goes down as an option gets closer to expiration, so the further out in time an option is the larger the vega.

Vega is an important risk tool in deciding where to buy and sell volatility, particularly when considering out months (longer time to expiration). In the out months, volatility has more of a chance to return to the historical mean, so when considering a trade you might want to consider a volatility chart to see if the implied volatility you are buying or selling out there is higher or lower than historical. If you are buying 80 implied volatility in the 3 month out options and 90 day historical volatility has been under 65 all year then there is a good chance it is going to come in between now and and then and your options will be worth less. Traders must always be balancing time versus cost.

Vega is another important tool in considering your portfolio versus the market as a whole. In a volatile market with the VIX, the market volatility index which measures the implied volatility of S&P 500 index options, trading high, you might want to be long a little gamma to take advantage of the current movement, but you may not want to be long much vega as the probability is that over time the volatility will return to more normal levels. We will discuss this more when we get to time spreads.

Rho
Rho measures the change in an options price with a change in interest rates. It is the least used of the Greeks so we won’t discuss it.

Dividends and Short Interest
Two other things which affect option price are dividends and short interest rate on hard-to-borrow stocks. It is very important to keep these in mind and to make sure that your information is accurate and that your inputs are up to date. In general if something seems too good to be true, you should back up and double check that there hasn’t been a new dividend announcement or that your stock has not become harder-to-borrow.

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