Assessing the performance of the VaR models on nonlinear portfolio - ZHU, Guantao (2013)
This paper aims to assess the performance of the VaR models on nonlinear portfolio. Historical Simulation, Monte-Carlo simulation and Delta-Gamma –normal model are implemented to estimate the daily VaR of a nonlinear portfolio consisting of two European Call options from 01/10/2012 to 13/09/2013. The underlying assets are NDX-100 index and S&P 500 index. Rolling over method is applied with a 500-day window. Daily volatility of the underlying risk factor is estimated by the implied volatility. The value of option is estimated using the Black-Scholes model. The normality of the risk factors is tested using the QQ-plot. Testing results show the change of the price is not normal distributed for both the two indexes. Monte-Carlo simulation gives a lower VaR compared with the other two methods. Unconditional coverage test, independence test and conditional coverage test are utilized to test the accuracy of the VaR estimations produced by the VaR models. The results indicate that Monte-Carlo simulation has a better performance in this specific case. Historical simulation and Delta-gamma model fails to estimate the right VaR because of their particular assumptions and the way they estimate VaR.