Transformational Approach to Analytical Value-at-Risk for near Normal Distributions

Abstract

In this paper, we extend the parametric approach of VaR estimation that is based upon the application of two transforms, one for handling skewness and other for kurtosis. These transformations restore normality to data when applied in succession. The transforms are well defined and offer an alternative to VaR models based on the variance–covariance approach. We demonstrate the application of the technique using three pairs of uncorrelated but negatively skewed and fat-tailed stock return distributions, one pair each from recent periods in US and international market, and one from the stressed period of US economic history. Furthermore, we extend the analysis to economic domain by calculating expected shortfalls and risk capital under different estimation methods. For the sake of completion, we compare the estimation results of normal and transformation methods to non-parametric historical simulation.

On Mixed Model for Improvement in Stock Price Forecasting

“…Based on the random walking model's accuracy of stock prediction, a random walking model based on Geometric Brownian Motion(BM)is used. The geometric Brownian motion model has two parameter drift terms and diffusion(fluctuations), which are very similar to the random walk through model structure with a drift term.In contrast the jump-diffusion model is based on the diffusion model of standard geometric Brownian motion (GBM) [21]. The prediction formula of geometric Browan motion after Euler dispersion is Eq.…”