Monte-Carlo VaR
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Monte Carlo VaR Introduction
Value at Risk (VaR) is a risk measure that quantifies the potential loss of a portfolio over a given time horizon at a certain confidence level. Monte Carlo (MC) VaR uses Monte Carlo simulations to generate profit and loss (P&L) scenarios, from which 1-day VaR at 99% confidence level is obtained and scaled to 10-day VaR.
In MC simulations, the parameters of the probability distributions are calibrated to historical data. The simulated risk factor scenarios are converted into market observable instrument risk factor scenarios and applied to full revaluation models.
Assuming that there are 10,000 scenarios, the 99% VaR can be obtained by sorting all the P&L scenarios and choosing the 100th worst observation.
VaR proxy is the usage of alternative method or data in VaR calculations when appropriate method or data is unavailable. VaR proxies are classified into two categories: model proxies and market data proxies. Model proxies are the use of alternative pricing models for independent valuation, risk measurement and VaR/Stress purposes. Market data proxies are the use of alternative market data when the appropriate market data are not available.
Risk factors (RFs) are the placeholders to take market data as model input. Market data proxies are implemented at RF levels. There are two types of RFs: market risk factors and simulation risk factors. Market Risk Factors (MRF) are designed to be consistent with the market instrument data used for pricing and calculating sensitivities while simulation risk factors (SRF) are not necessary aligned but intended only as a representation of the market risk factors as a compromise for computational performance and accuracy of simulations.
The calibration procedure is designed to analyze historical market data and the statistical relationship among various market driving factors. The calibration risk factor selection and processing are designed to cover the general market risk. For specific deals, only the statistics related to general market risk are calculated, whereas the idiosyncratic risk portion is not considered.
Risk factor raw returns are calculated from the risk factor raw prices, while the risk factor clean returns are calculated from risk factor clean prices. Some risk factor returns are based on absolute returns, while others based on relative returns.
Assume that risk factors (RFs) follow a stochastic model that should be capable of producing a wide range of distributions, including ones with fat-tails, and reproducing correlation structures. The parameters of the probability distribution (volatilities, correlation matrix) are calibrated using robust estimation techniques to improve the tolerance to outliers.
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