The “Greeks” are a measure of the sensitivity of the option price to small changes in the main inputs to the pricing model: price, volatility, time (until expiration), and interest rate. Other than the mention of “Rho” below, I’m excluding interest from further discussion because at current rates it is largely irrelevant. These Greeks generally need to be calculated by some kind of modeling software.
Let’s now explore Delta, Gamma, Vega, Theta and Rho to gain a better understanding of some of the factors influencing option pricing.
Delta tells us how much the option price is expected to move compared to the underlying security, generating a positive value for calls and a negative one for puts. It is usually expressed as a decimal (eg .75), sometimes expressed as a stock equivalent (eg .75 * 100 shares = 75 deltas). So a .75 delta call would move approximately .75 for a 1.00 up-move in the underlying, -.75 for a 1.00 down-move. I say approximately because delta is not static, it changes with price movement (see “Gamma”) as well as with changes in volatility and time.
At this point some general observations about delta can be made:
- At-the-money (“ATM”) options are about +/- .50.
- The deeper in-the-money (“ITM”), the more the options approach +/- 1.00.
- The further out-of-the-money (“OTM”), the more the options approach +/- .00.
Nearer term ITM options have larger absolute value delta than a same strike further term. Near term OTM options have smaller absolute value delta than further term. The lower the volatility, the faster options approach +/- 0.00/1.00 as they move away from ATM; the higher the volatility, the more all options approach +/- .50.
Delta is so important among the Greeks that it actually has its own Greek – Gamma. Gamma measures how fast the delta changes with stock price movement. ATM options have the largest gamma, while gamma declines as the option moves away from ATM. Nearer term options have more gamma than the same strike price further term option. One way to remember this is to think about an ATM option one trade away from expiring, a one tick move either way changes it to 0.00/1.00 delta.
Vega gives us an idea of how much the option price would move with a 1% change in volatility. This has more use in trading options against other options than in using options as a stock equivalent. ATM options will have the most vega, and vega will decrease as the options move in or out of the money. For the same strike price, further term options will have more vega. Please note that the volatility used here is not historic (or statistical) volatility which is an exact number based on price history, but rather a forecast volatility, the marketplace’s best guess as to the future volatility. “Implied volatility” is calculated by using the option price as an input to the model and returning the volatility that implies.
Theta is a measure of how much the option price loses in 1 day. Its value can be approximated as the extrinsic value (essentially vega) divided by the number of days until expiration. So ATM options decay the most. Nearer term options decay faster, with the number of days being a more important factor than the extrinsic value.
Rho indicates how much the option price will change with a 1% change in interest rate. For now, this is just something to keep in the back of your mind, and revisit if/when interest rates become relevant again in the future.
It’s important to note that the greeks are additive in nature. When I say additive I mean that the total delta exposure for all the options on an underlying vehicle can be found by adding the delta of each individual option. In looking at the core simplified level, we see that a positive greek value means that the options price benefits from an up-move in that specific model input, while the opposite is true as well for a negative value.
For our purposes, we will be using options as a stock equivalent, so the most important Greeks are delta and theta. Delta establishes our expectations for absolute return relative to the stock and gives us a value that we can use to calculate how much leverage we need to achieve equal market exposure as the underlying stock. Theta tells us how much we are paying (for long options) or collecting (for short options) in whatever strategy we are using for a stock equivalent. This directly connects us to the next topic we’ll be covering in our series; join us next time as we cover the basic options trading strategies and their characteristics.
If you’d like to start trading options with precision based on grounded in quantified test results, we encourage you click here and register for the Quantified Options Trading Strategies Summit 2013. This is a live event where you’ll have the opportunity to directly pose your questions to Larry Connors and the Connors Research staff.