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ON THE USE OF REALIZED QUASI-MONTE CARLO METHOD IN EUROPEAN OPTION PRICING
Seki Kim,Doobae Jeon 한국산업응용수학회 2006 한국산업응용수학회 학술대회 논문집 Vol.1 No.2
The pricing of options is a very important problem encountered in complex financial markets. The famous Black-Scholes model provides explicit closed form solutions for the values of European call and put options. But for many other options, either there are no closed form solutions, or if such closed form solution exist, the formulas exhibiting them are complicated and difficult to evaluate accurately by conventional methods. In this case, Monte Carlo methods may prove to be valuable. Monte Carlo methods are often used when other methods are difficult to implement due to the complexity of the problem. The disadvantages of Monte Carlo Methods are that the error term is probability and that it can be computationally burdensome to achieve a high level of accuracy. Quasi-Monte Carlo is technique for improving the efficiency of the Monte Carlo Method. Under the conventional approach pseudo-random numbers yields an error bound that is probabilistic which can be a disadvantage. Another drawback of the standard approach is that many simulations may be required to obtain a high level of accuracy. Quasi-Monte Carlo Methods use sequences that are deterministic instead of random. These sequences improve convergence and give rise to deterministic error bounds. But these Methods have some limits which does not reflect the trend of rise, fall and hold. We divide 2-dimensional space into three parts. Each three parts indicate rise, fall and hold. If this trend apply to the Quasi-Monte Carlo Methods, it may be better than the known Methods.
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