### Monte Carlo Value at Risk

Value at Risk (VaR) is the regulatory measurement for assessing market risk. It reports the maximum likely loss on a portfolio for a given probability defined as x% confidence level over N days. VaR is vital in market risk management and control. Also regulatory and economic capital computation is based on VaR results. Although VaR measure is objective and intuitive, it doesn’t capture tail risk. There are three commonly used methodologies to calculate VaR – parametric, historical simulation and Monte Carlo simulation. This presentation focuses on Monte Carlo VaR.

Monte Carlo VaR assumes market factors follow certain stochastic processes. It has easy back and stress test and is good for high confidence level and tail risk. The drawbacks are dependent on distribution assumption and calibration is required. Most importantly it requires extensive computation.

VaR is computed using risk sensitivities from the official risk systems. Consideration must be paid to what impact these adjustments may have, if any, to these risk sensitivities. For example, a large IPV may signal a material difference between the market data in the source system and the independent market data. The source system data is used to compute the risk sensitivities for VaR.

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