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Article

A Fast Monte Carlo Algorithm for Estimating Value at Risk and Expected Shortfall

Ming-Hua Hsieh, Wei-Cheng Liao and Chuen-Lung Chen
The Journal of Derivatives Winter 2014, 22 (2) 50-66; DOI: https://doi.org/10.3905/jod.2014.22.2.050
Ming-Hua Hsieh
is an associate professor in the Department of Risk Management and Insurance at National Chengchi University in Taiwan.
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  • For correspondence: mhsieh@nccu.edu.tw
Wei-Cheng Liao
is a Ph.D candidate in the Department of Management Information Systems at National Chengchi University in Taiwan.
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  • For correspondence: 97356505@nccu.edu.tw
Chuen-Lung Chen
is a professor in the Department of Management Information Systems at National Chengchi University in Taiwan.
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  • For correspondence: chencl@nccu.edu.tw
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Abstract

Risk management today focuses heavily on estimating the location and conditional expectation of the left tail of the probability distribution for returns or portfolio value. The Holy Grail in derivatives pricing is a closed-form valuation equation such as in the Black–Scholes model, which takes a small number of input parameters and produces the exact arbitrage-free properties of the target portfolio, including value-at-risk (VaR) and expected shortfall (ES). But closed-form solutions are rare and largely limited to highly idealized markets. Lattice-based approximation techniques are available for more general settings, but they also have serious constraints. When all else fails, there is Monte Carlo simulation. Simulation always works, in principle, but the amount of calculation required in practice can be tremendous, which provides a strong incentive to find ways to speed up the process. Antithetic variates, control variates, and importance sampling are all helpful. In this article, the authors propose a new technique for estimating VaR and ES that is simple but remarkably powerful. Their first step is to determine which underlying risk factor is the most important. Next, for each simulated value of this primary factor, they simulate values for the remaining factors, requiring that every path generated exceed the VaR threshold. By not computing numerous paths that do not end up in the tail, the procedure can achieve the same accuracy as standard Monte Carlo simulation but several orders of magnitude faster.

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The Journal of Derivatives: 22 (2)
The Journal of Derivatives
Vol. 22, Issue 2
Winter 2014
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A Fast Monte Carlo Algorithm for Estimating Value at Risk and Expected Shortfall
Ming-Hua Hsieh, Wei-Cheng Liao, Chuen-Lung Chen
The Journal of Derivatives Nov 2014, 22 (2) 50-66; DOI: 10.3905/jod.2014.22.2.050

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A Fast Monte Carlo Algorithm for Estimating Value at Risk and Expected Shortfall
Ming-Hua Hsieh, Wei-Cheng Liao, Chuen-Lung Chen
The Journal of Derivatives Nov 2014, 22 (2) 50-66; DOI: 10.3905/jod.2014.22.2.050
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