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+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)