Numerical Analysis Of Two-Dimension Discrete Barrrier Option Pricing

As one of the most common exotic options,barrier option has a very important part in theory and practice.So,it becomes a hotspot of research.But former research is most common in one-asset option.Although they expand their research from different directions,they change the property of the barrier mostly,so they can get different results.For the increasing of the number of assets,it is seldom even in two-assets conditions.This thesis does some expansions to the classical barrier options.The number of underlying assets is increasing to 2.Furthermore,the observing of barrier is assuming to be discrete.First,the existing result of one-asset option is checked.It is certainly accurate in most conditions.Then we start researching the two-assets options.Two classical numerical methods are used,specifically,Monte Carlo simulation and binomial trees.For each method,we change the parameters such as knock-out conditions,payoff functions and numbers of observing to investigate their effects to the price of option.For Monte Carlo method,we improve the original method by antithetic variables.The result is the convergence of Monte Carlo method is fairly good,and the speed of the convergence is fast.But when the number of simulations is much,the computing speed is rather slow.We discover the price of option is logarithmic decreasing with the increasing of number of observing.The method of antithetic variables can improve the classical method in convergence speed,computing speed,etcFor binomial trees,the speed of convergence is relatively slow.And the price has a drastic fluctuation.The price of binomial trees has some differences with the Monte Carlo method,too.But by changing the parameters,we discover the range of the price changing with parameters is similar to Monte Carlo method.So,this method has certain rationality.But the reason of unusual convergence pattern is still unknown.More researches are needed for this reason.The reason of two different prices of different methods is also strange,and more researches are needed,too.This thesis does some investigation to these two problems,too.Finally,we summarize the work of this thesis,and do some prospects of the possible research directions in the future.