Parallel computing with improved techniques for Monte Carlo simulation in VaR

Value at Risk ( VaR ) is a widely used tool for the assessment of one’s investments. VaR is used to evaluate the risk of loss on a financial portfolio. This metric can be computed in several ways. In the historical approach, past trends of the appropriate combination of stocks is used to estimate current portfolio fluctuations. The variance – covariance method, meanwhile, seeks to discover relationships in price fluctuations for one’s stocks. Finally, Monte Carlo simulation capitalizes upon the stochastic nature of stock prices to predict future value. This latter approach, however, relies heavily on the multiplication of vectors with matrices and is therefore time consuming. An investor always has a predetermined limit in mind of how much they can afford to lose – this quantity is called collateral. This limit is often agreed upon via consultation with a risk manager. The VaR decision problem seeks to answer this question: Does VaR exceed an investor’s collateral? The loss matrix of a portfolio contains valuable information that may be gleaned via the use of norms. This thesis focuses on computing upper bounds for VaR which rely upon information obtained from these norms; we thereby can discern when it is possible to answer the VaR decision problem without resorting to time-consuming Monte Carlo methods. We use a parallel computing architecture – CUDA in this thesis. Several CUDA kernels are implemented and executed on a Nvidia graphics card thereby increasing computational performance