A Computationally more Efficient Distance based VaR Methodology for Real Time Market Risk Measurement

Abstract

Measurement of market risk requires lots of computational resources when the Value-at-Risk (VaR) is computed using the historical simulation approach as it involves full revaluation of the portfolio for the considered data points. Although approximations can be done using the delta-normal, delta-gamma and delta-gamma-theta approaches, historical simulation approach alone is straight forward method that uses past data to generate future values without assuming any distribution for the underlying returns. The requirement of intensive computational effort in case of historical simulation hinders it’s usage for applying to real time VaR calculation. In this work we propose a methodology that doesn’t forego the benefits of historical simulation approach but can be applied to calculate market risk VaR in real time. The VaR calculated using the proposed methodology converges as the range of the portfolio returns is increased. The proposed methodology is also superior to the historical simulation approach in terms of usage of the computational resources and applicability to real time without sacrificing accuracy obtained using historical simulation approach.