Chapter 40: Atlvanced Concepts 859 
sense when one notes that there are extra long calls and they would be getting deep­
er in-the-money as the stock moves up. Conversely, if XYZ continues to move lower, 
the delta will continue to decrease and will quickly become negative, meaning that 
the position would become short overall. Hence, the position does indeed resemble 
a long straddle: It gets longer as the market moves up and it gets shorter as the mar­
ket moves down. 
Long options, whether puts or calls, have positive gamma, while short options 
have negative gamma. Thus, a strategist with a position that has positive gamma has 
a net long option position and is generally hoping for large market movements. 
Conversely, if one has a position with negative gamma, it means he has shorted 
options and wants the market to remain fairly stable. 
Note that it is possible to be delta neutral, but to have a significant gamma. (For 
example, if one owns puts and calls with offsetting deltas, he would be delta neutral, 
but would have positive gamma since both options are long.) If one is delta neutral, 
he knows he has no market exposure at this time, but his gamma will show him what 
exposure his position will acquire as the market moves. These concepts will be dis­
cussed in greater detail later in this chapter. 
VEGA OR TAU 
There is no letter in the Greek alphabet called "vega." Thus, some strategists, being 
purists, prefer to use a real Greek letter, "tau," to refer to this risk measurement. The 
term "vega" will be used in this book, but the reader should note that "tau" means 
the same thing. Vega is the arrwunt by which the option price changes when the 
volatility changes. Vega is always expressed as a positive number, whether it refers to 
a put or a call. 
It is known that more volatile stocks have more expensive options. Thus, as 
volatility increases, the price of an option will rise. If volatility falls, the price of the 
option will fall as well. The vega is merely an attempt to quantify how much the 
option price will increase or decrease as the volatility moves, all other factors being 
equal. 
Before considering an example, a review of the term volatility is in order. 
Volatility is a measure of how quickly the underlying security moves around. 
Statistically, it is usually calculated as the standard deviation of stock prices over some 
period of time, generally annualized. This statistical measure is expressed as a per­
cent, although relating that percent to actual stock movements can be complicated. 
Suffice it to say that a stock that has a 50% volatility is more volatile than a stock with 
30% volatility. The stock market generally has a volatility of about 15% overall, 
although that may change from time to time (crashes, for example).