Chapter 40: Advanced Concepts 
FIGURE 40-19. 
Trading long gamma, 11 conventional" calendar. 
7500 
5000 
2500 
fJ) 
fJ) 
.3 :;:, 0 '§ 45 50 Q. 
-2500 
-5000 At March Expiration 
-7500 
Stock Price 
901 
75 
much risk of time decay. A second attempt was made, introducing positive volatility 
into the situation, but that didn't seem to help much. Finally, a third analysis was gen­
erated involving only long volatility and not long gamma. The resulting position has lit­
tle time risk, but has risk if the stock drops in price. It is probably the best of the three. 
The strategist arrives at this conclusion through a logical process of analysis. 
ADVANCED MATHEMATICAL CONCEPTS 
The remainder of this chapter is a short adjunct to Chapter 28 on mathematical 
applications. It is quite technical. Those who desire to understand the basic concepts 
behind the risk measures and perhaps to utilize them in more advanced ways will be 
interested in what follows. 
CALCULATING THE "'GREEKS" 
It is known that the equation for delta is a direct byproduct of the Black-Scholes 
model calculation: 
~ = N(dl)