More precise estimation methods for the risk and the risk contribution of a portfolio consisting of financial instruments

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I propose a much more precise estimation method for the risk and the risk contribution (the contribution of each asset for the risk of the portfolio) than the Monte Carlo method often used in the risk evaluation models. By using "hybrid method" in which the Monte Carlo simulation and the analytical approximate formula (the saddlepoint approximation) are combined, we can estimate precisely not only the famous risk measure "VaR" (Value at Risk) but also"ES" (Expected Shortfall) which has theoretically excellent properties as a risk measure.