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Using the Black-Scholes model, we also construct the aggregate delta and aggregate gamma as the input to the Quantlet. 01 confidence level, 1 days forecast horizon and 1,000 times of simulation, the result of the estimation is as follows. 24% of portfolio value with less than 1% probability in 1 day. However, the key question of the empirical example is that how much variance reduction is achieved by the different sampling methods. 5 Variance Reduction Techniques in Monte-Carlo Simulation 31 times and estimated the standard error of the estimated VaR for each sampling method.
T . d. random variables S (t) . The first step will be to determine the parameters of the marginal distributions. In the numerical example we will use the normal distribution N(0, σi2 ), and estimate the volatility σi using an equally weighted (t) 2 (t) (t) (t−1) T 1 ) volatility estimator σ ˆi2 = T −1 t=2 (ri ) of the returns ri = log(si /si for simplicity. The marginal distributions of the risk factors are then lognormal. The remaining task is to estimate the copula parameters. In the XploRe VaR quantlib this is done by the function res = VaRfitcopula(history,copula,method) fits the copula to the history using fitting function method.
And 32 1 Approximating Value at Risk in Conditional Gaussian Models Sorensen, D. (1999). LAPACK Users’ Guide, third edn, SIAM. org/lapack/lug/. Basel Committee on Banking Supervision (1995). pdf. , Broadie, M. and Glasserman, P. (1998). Monte Carlo methods for security pricing, Journal of Economic Dynamics and Control 3: 1267– 1321. , Eberlein, E. and Kokic, P. (2000). A tailored suit for risk management: Hyperbolic model, in J. Franke, W. H¨ardle and G. Stahl (eds), Measuring Risk in Complex Stochastic Systems, Vol.