| Summary: | 碩士 === 國立中央大學 === 財務管理研究所 === 89 === For many complex options, analytical solutions are not available. In these cases a Monte Carlo simulation is an important numerical method. In its basic form, however, the Monte Carlo simulation is computationally inefficient, the control variate technique can be used to improve the efficiency of a Monte Carlo simulation. This paper presents a principle for finding better control variates when considering an option.
A good control variate has to satisfy two conditions: The first is that a good control variate satisfies the same PDE satisfied by the target option. The second is that the boundary condition for the control variate is similar to the boundary condition for the target option. Options under consideration in this paper include American put options, barrier options, Asian options, and spread options. The result shows that a good control variate can improve the efficiency of the simulation dramatically and a good control variate can be differentiated from a bad control variate in a Monte Carlo simulation.
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