The High Order Greeks Of The Exotic Options

In the study of the options,Greeks are widely studied by lots of researchers.Compared to the common European options,exotic options can't get explicit expressions of their prices or Greeks.So we need to estimate them by numerical simulations.In this thesis,we studied the Gamma of two exotic options:Asian digital options and lookback options.The main difficulty of this problem is that the payoff functions of the exotic options are not continuous so that some common methods can't be used or have large errors.So we have to use some improved methods to estimate them.In this thesis,we mainly used the LR method and the kernel estimation method to complete the Gamma estimation of these exotic optionsBesides,we use QMC simulation method into the numerical estimation and compared it to the traditional MC method.We draw some conclusions as following.First,kernel estimation method is better than the LR method.Second,QMC simulation method can improve the precision of the LR method largely.Third,QMC simulation method can't improve the precision of the kernel estimation when it is used to the Asian digital options.Finally,as for the lookback options,QMC method is more effective in the lower dimension,but fails in the higher dimension.