Greece, an amazing and dynamic culture, gave us some of the greatest thinkers of our time, Plato and Socrates. Monumental literature, such as The Iliad and The Odyssey. Greek cuisine, such as moussaka, stifado, Greek salad, spanakopita and the world famous souvlaki. Sweet deserts such as galaktoboureko, ouzo, and metaxa. Greek gods and goddesses Zeus, Hera, Poseidon, Ares, Athena, Apollo, and Aphrodite.
However, this article is not about the history of Greece and its debt crisis, but rather how the financial Greeks can make you money and help you to understand the movement of option derivatives.
Let's get to the basics of what first-order greeks are, and what they mean. The price of options are typically determined by the black-scholes model or a binomial lattice. These prices are set by the option market makers and include the following inputs, implied volatility, stock price, strike price, days to expiration, and the interest rate. For example, here is how the Cisco (CSCO) December $19 call is priced as of today, 11/17/2011:
Delta = DV/DX is the rate of change in which an option will change for a $1 move in the stock. In this case if Cisco were to rise to 19.39, holding the implied volatility constant, the option would simultaneously rise from .40 + .37 = .77.
Gamma = DV/DX^2 is the rate of change the Delta will change for a $1 move in the stock. This is a measure of the curvature of the delta. If Cisco were to rise to 19.39, the delta would simultaneously change from .3730 + .2323 = .6053
Theta = DV/DT is the amount the option will decay as one day passes. In this case, this option will decay 0.01 daily until expiration day arises.
Vega = DV/Dsigma is the amount the option price will rise for a 1% rise in volatility. In this case if the Implied Volatility were to rise to 35, the option would rise from .40 + 4.08*(.02) = .4816.
Rho = Is the rate of change of the option for a change in interest rate. This function typically has little weight since options by nature are short-term it usually doesn't affect the value of the option at all.
Now you might wonder: What does this mean if I am long a call? Well, you can see specific scenarios for your option. For example, the Cisco December 17 $19 call expires in 30 days; I know that the option will decay 1 cent daily and accelerate the closer it gets to expiration. If Cisco were to open up $1 today, your option would rise 37cents and continue to rise higher due to the gamma function of 23 cents.
The higher the gamma is, the closer it is to the money, and the more it is affected by the stock price.
Now if I were to short this call, I would pocket the 40 cents and simply watch 1 cent tick off daily. The trick to shorting an option is to find one with the highest implied volatility, highest theta, and lowest gamma.
The term "Delta-neutral" implies all your delta's equal zero, but what is it and how can you use it for your advantage? A perfectly Delta-Netural stock position would be long and short the same number of shares of the same stock at the same time. No matter what the stock did, the overall position would not gain or lose.
Whenever you are long or short a stock you are exposed to delta, that is the amount that your stock will change for a $1 change. Option deltas and Stocks delta are essentially the same concept, however, Stocks are not affected by Gamma or Theta. So if you were long 1000 shares of Cisco at $18.39 your net Investment is $18,390 and your Delta is now -1000.
In order to guard against the stock of Cisco falling another dollar you could buy an offsetting amount of puts to hedge against your position being exposed to a loss, which if done perfectly would mean the value of your portfolio would not change in value.
In conclusion, never trade options without first looking at the greeks of the option. I've heard this one many times before, and I'm sure you have too: "I think Netflix is going to go up, should I buy calls?" The stock may go up and you can still lose money; therefore, always pay attention to the Greeks and the implied volatility before entering into an option trade. Options are not like stocks; you have to guard against implied volatility, decay, first-order Deltas, and second-order Gammas.