GAMMA IN 4DIMENSIONS A good option trader has to think about his option Greeks in at least 4dimensions to 5 dimensions. Here the gamma calculated with volatility changing from 12% to 50% (flat vol surface, Strike 100, rate 10%, volatility from 12% to 50%.). Have in mind that in practice implied volatility is more than "volatility". Only in the BlackScholesMerton world where close to all risk can be removed by delta hedging the volatility is the markets best estimate on future realized standard deviation. In practice the implied volatility is a basket factor containing also supplydemand situation for that particular options, a jump in demand can give a upjump in implied volatility etc., much more on this in chapter 2 of my book Derivatives Models on Models, see also KnowYourWeapon 1 and 2 (that also comes with book and part 1 can be found on the web as well, www.wilmott.com) A great option trader should know in his guts where any Greek will move for any movement in the asset, the so called implied volatility and for time moving by. Option trading is a multidimensional experience beyond any other type of trading. 
Copyright Espen Haug 1998 2008 all rights reserved
