Using quasi-Monte Carlo methods to evaluate value-at-risk

Abstract

<P>THIS IS THESIS WILL PROVIDE SOME SIMULATION METHODS FOR VALUE-AT-RISK(VAR) CALCULATION USING THE QUASI-MONTE CARLO(QMC) METHOD, WHICH HAS BEEN USED AS AN EFFICIENT COMPUTATIONAL VEHICLE IN THE AREA OF FINANCE. THE PURPOSE OF THIS THESIS IS TO FIND OUT HOW MUCH IMPROVEMENT CAN BE MADE THROUGH THE QUASI-MONTE CARLO METHOD. LIKE OTHER FINANCIAL PROBLEMS, THE VALUE-AT-RISK PROBLEM CAN BE TRANSFORMED INTO A VALUATION OF AN INTEGRAL, WHICH WILL BE SHOWN IN OUT METHODS, NAMELY, THE CONDITIONAL EXPECTATION METHOD AND THE FOURIER TRANSFORMATION METHOD. FOR THE VARIANCE REDUCTION CONCERN, WE INTRODUCE LOW-DISCREPANCY SEQUENCES, HALTON, FAURE, AND SOBOL SEQUENCES. IN ORDER TO COMBINE THE HIGHER ACCURACY OF QMC WITH PRACTICAL ERROR ESTIMATION OF MONTE CARLO METHDS, DIFFERENT RANDOMIZATION TECHNIQUES WILL BE APPLIED TO THESE SEQUENCES AS WELL. NUMERICAL EXPERIMENTS ARE GIVEN IN THE LAST CHAPTER OF THIS THESIS.</P>