Efficient Monte Carlo methods for evaluating the downside risk of financial positions

Abstract

In finance there is an amount of uncertainty and risk involved with valuing the future value of figures. One technique that leads to the reduction of this uncertainty is Monte Carlo simulation. Different methods have been proposed to speed up the convergence of standard Monte Carlo, and this dissertation explores the Quasi-Monte Carlo method based on low discrepancy sequences. Various low discrepancy sequences are introduced and investigated, together with the provision of a method of estimating Value at Risk with more accuracy, by In finance there is an amount of uncertainty and risk involved with valuing the future value of figures. One technique that leads to the reduction of this uncertainty is Monte Carlo simulation. Different methods have been proposed to speed up the convergence of standard Monte Carlo, and this dissertation explores the Quasi-Monte Carlo method based on low discrepancy sequences. Various low discrepancy sequences are introduced and investigated, together with the provision of a method of estimating Value at Risk with more accuracy, by In finance there is an amount of uncertainty and risk involved with valuing the future value of figures. One technique that leads to the reduction of this uncertainty is Monte Carlo simulation. Different methods have been proposed to speed up the convergence of standard Monte Carlo, and this dissertation explores the Quasi-Monte Carlo method based on low discrepancy sequences. Various low discrepancy sequences are introduced and investigated, together with the provision of a method of estimating Value at Risk with more accuracy, by means of the Sobol sequence.