Abstract

VaR is a popular measure for benchmarking market risk based on price or return fluctuations of instruments among institutions. Calculation of VaR depends very much on the model explaining the price changes and volatility of the underlying assets. However, theoretical models can be very unrealistic in comparison to actual historical data. Modifications are required in order for the models to better fit the actual market conditions. If finding a mathematical tool to bridge to theoretical model with reality were possible, we could expect a better or less expensive estimation of the VaR. Calculation of the actual VaR for an asset can be started by first finding the risk adjusted return under the assumption of a theoretical return model covered by the risk neutral measure, where a new mathematical tool could link the risk adjusted models back to the actual measure. We propose a distortion operator to serve as such a bridge between the actual and risk neutral distributions.