Calculation aspects of the European Rebalanced Basket Option using Monte Carlo methods

ENGLISH ABSTRACT: Life insurance and pension funds offer a wide range of products that are invested in a mix ofassets. These portfolios (II), underlying the products, are rebalanced back to predetermined fixedproportions on a regular basis. This is done by selling the better performing assets and buying theworse performing assets. Life insurance or pension fund contracts can offer the client a minimumpayout guarantee on the contract by charging them an extra premium (a). This problem can bechanged to that of the pricing of a put option with underlying . It forms a liability for the insurancefirm, and therefore needs to be managed in terms of risks as well. This can be done by studying theoption’s sensitivities. In this thesis the premium and sensitivities of this put option are calculated,using different Monte Carlo methods, in order to find the most efficient method.Using general Monte Carlo methods, a simplistic pricing method is found which is refined by applyingmathematical techniques so that the computational time is reduced significantly. After consideringAntithetic Variables, Control Variates and Latin Hypercube Sampling as variance reduction techniques,option prices as Control Variates prove to reduce the error of the refined method mostefficiently. This is improved by considering different Quasi-Monte Carlo techniques, namely Halton,Faure, normal Sobol’ and other randomised Sobol’ sequences. Owen and Faure-Tezuke typerandomised Sobol’ sequences improved the convergence of the estimator the most efficiently. Furthermore,the best methods between Pathwise Derivatives Estimates and Finite Difference Approximationsfor estimating sensitivities of this option are found.Therefore by using the refined pricing method with option prices as Control Variates together withOwen and Faure-Tezuke type randomised Sobol’ sequences as a Quasi-Monte Carlo method, moreefficient methods to price this option (compared to simplistic Monte Carlo methods) are obtained.In addition, more efficient sensitivity estimators are obtained to help manage risks.