The variance of the estimation of the probability γ that an event occurs using IID Monte Carlo Methods is inversely proportional to the sample... Show moreThe variance of the estimation of the probability γ that an event occurs using IID Monte Carlo Methods is inversely proportional to the sample size M, Var[ˆγ] = γ(1 − γ)/M. If we fix the relative standard deviation at 10% when estimating the probability of a rare event γ ≪ 1, the necessary sample size may reach values that are computationally not acceptable. This is very common in the Finance Industry when trying to estimate the joint default probabilities of 15 stocks in a portfolio of 100 stocks. De Moral and Patras [1] presented a new variance reduction technique called Interacting Path System (IPaS), which showed to be very efficient in a rare event situation. Our objective is to run some simulations in order to verify its efficiency against other variance reduction techniques found in the literature as well as implement new modifications using quasi-Monte Carlo methods in order to increase its efficiency. We run several simulations of rare and non-rare scenarios using IID Monte Carlo methods, quasi-Monte Carlo Methods and IPaS for the purpose of estimating the efficiency of IPaS. Moreover, we modified the current IPaS algorithm and implemented low discrepancy points in order to obtain a better estimator. We have found that IPaS technique is indeed more efficient than the well-known estimators in rare event scenarios, but quasi Monte Carlo methods is preferable if it is not a rare event. In addition to this, we have shown that the modified IPaS is even better than IPaS technique under rare event cases and it is similar to quasi Monte Carlo methods under non-rare events. However, in problems with higher dimensions, the efficiency of modified IPaS does not differ from IPaS results. M.S. in Applied Mathematics, July 2013 Show less
