Sampling descriptive appraisal of options in Europe through Monte Carlo simulation: the effect of dimensionality and the likelihood of exercise in the gain of precision

The purpose of this paper is to evaluate the effect of dimensionality and probability of exercise of a European call option on the precision improvements obtained by the usage of Descriptive Sampling on a Monte Carlo Simulation to price such derivative as opposed to the use of traditional Simple Random Sampling. After verifying the absence of bias, the precision of the estimates was assessed by their standard error. The results show that the statistical efficiency of both techniques is unaffected by an increase of dimensionality and maintain their level of precision. However, as to the exercise price, although Descriptive Sampling proved to be more efficient than Simple Random Sampling, the improvement weakens as the options exercise probability declines. Although this work relates to European options, other options should behave similarly in regard to dimensionality and exercise price.