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(1) Delta-Normal Method
The delta-normal method assumes that all asset returns are normally distributed. As the portfolio return is a linear combination of normal variables, it is also normally distributed. This method consists of going back in time, e.g. over the last 5 years, and computing variances and correlations for all risk factors. Portfolio risk is then generated by a combination of linear exposures to many factors that are assumed to be normally distributed, and by the forecast of the covariance matrix.
Required:
(1) for each risk factor, forecasts of volatility and correlations
(These data can be downloaded from the RiskMetrics site, originally developed by JP Morgan)
(2) positions on risk factors.
(2) Historical-Simulation Method
This method consists of going back in time, e.g. over the last 5 years, and applying current weights to a time-series of historical asset returns. This return does not represent an actual portfolio but rather reconstructs the history of a hypothetical portfolio using the current position. Of course, if asset returns are all normally distributed, the VAR obtained under the historical-simulation method should be the same as that under the delta-normal method.
Required:
(1) for each risk factor, a time-series of actual movements, and
(2) positions on risk factors.
(3) Monte Carlo Method
Monte Carlo simulations proceed in two steps.
First, the risk manager specifies a stochastic process for financial variables as well as process parameters; the choice of distributions and parameters such as risk and correlations can be derived from historical data.
Second, fictitious price paths are simulated for all variables of interest. At each horizon considered, which can go from one day to many months ahead, the portfolio is marked-to-market using full valuation. Each of these ``pseudo'' realizations is then used to compile a distribution of returns, from which a VAR figure can be measured.
Required:
(1) for each risk factor, specification of a stochastic process (i.e., distribution and parameters),
(2) valuation models for all assets in the portfolio, and
(3) positions on various securities.
三种方法除了协方差矩阵需要RiskMetric提供的服务之外,其他的都能根据样本数据计算啊,都不难啊,需要私下讨论的可以加我quantrisk@hotmail.com |
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