QMC Combing With IS On Numerical Simulation Of VaR And CVaR

This paper introduces basic conception of Value-at-risk and Conditional valueat-risk.After analyzing their propositions,we present di?culties in numerical simulation.Futhermore,we introduce Importance Sampling as a signi?cant method in variance reduction techniques.By describing and analyzing,we prove its e?ciency theoretically.After analyzing and describing relative algorithm,under traditional multivariate normal distribution model,we indicate superiority of quasi-monte carlo method combining with importance sampling in practical situation by some examples of numerical simulation.After that,we introduce heavy-tailed risk factors model,which is much closer to practical ?nancial data comparing with traditional multivariate normal distribution model.Then,we analyze propositions of heavy-tailed risk factors model and solve di?-culties under this new model by several indirect methods.Similarly,after analyzing and describing relative algorithm,under heavy-tailed risk factors model,we indicate superiority of quasi-monte carlo method combining with importance sampling in practical situation by some examples of numerical simulation.In the end,we conclude the e?ect of applying quasi-monte carlo methods and importance sampling in numerical simulation area and expect their meaning to later relative research in future.