Aplicação da Amostragem por Importância à Simulação de Opções Asiáticas Fora do Dinheiro

According to previous results, the main variance reduction techniques performed well during the Monte Carlo simulation of Asian calls (Marins, Santos e Saliby, 2003). Control Variate best performed in terms of the precision of the estimates, whereas Descriptive Sampling was the fastest technique. However, a performance deterioration was noted as the exercise probability of the Asian calls was decreased, or equivalently, as these calls became out of the money. In this the out of the money region, the call exercise becomes a rare event and the simulation process remains injured. One possible solution is to implement Importance Sampling, which is a specific technique to deal with rare event simulation problems. This technique has already performed well in the out of the money European call simulation case (Saliby, Marins and Santos, 2005). Therefore, the objective of this article is to use Importance Sampling in the simulation out of the money Asian calls, in order to verify if the precision of the estimates is preserved. It is also implemented a combination of Importance Sampling with the two previously mentioned best techniques, Control Variate and Descriptive Sampling. According to the main findings, Importance Sampling was not only crucial to allow simulation in the out of the money region, but also to provide additional precision gains when combined with the two other techniques.