中文摘要：

高维期权组合VaR值的计算时间和计算工作量随着市场风险因子维数的增加而迅速增加．为此，引入投影降维技术，用少数几个风险因子来解释高维期权组合总的风险，并结合快速卷积方法，建立了基于投影降维技术的市场风险因子呈厚尾分布情形下的期权组合非线性VaR模型，达到减少计算时间和计算工作量的目的，同时期权组合价值变化的信息又没有太大的损失．数值结果表明，投影降维技术能够达到与快速卷积方法、Monte—Carlo方法差不多的估算精度，而计算效率明显优于快速卷积方法、Monte—Carlo方法，计算时间和计算工作量明显减少．

英文摘要：

To obtain VaR of options portfolio with many dimensions, the calculation time and effort increases rapidly when market risk factors increase. For this reason, the paper introduces a projection dimension reduc- tion technique to compute VaR of the options portfolio, which uses a few risk factors to explain the total risk of the options portfolio with many dimensions. Moreover, the paper combines it with a fast convolution method, and establishes nonlinear VaR model of options portfolio based on projection dimension reduction technique with market risk factors having heavy-tailed distributions. As a result, the computation time and effort have been largely reduced, however, the information of the change in the options portfolio value has almost not been lost. Numerical results show that computational accuracy using projection dimension reduction technique is slightly different with that of fast convolution method or Monte Carlo simulation method. However, projection dimension reduction technique is more efficient than the fast convolution method or Monte Carlo simulation method of calculation, as its com~utation time a,r] effr, rt ~r~ ~;~,,;~;,.~1 4 a