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The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile

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  • Arjan Berkelaar
  • Phornchanok Cumperayot
  • Roy Kouwenberg

Abstract

Value‐at‐risk (VaR) has become the standard criterion for assessing risk in the financial industry. Given the widespread usage of VaR, it becomes increasingly important to study the effects of VaR based risk management on the prices of stocks and options. We solve a continuous‐time asset pricing model, based on Lucas (1978) and Basak and Shapiro (2001), to investigate these effects. We find that the presence of risk managers tends to reduce market volatility, as intended. However, in some cases VaR risk management undesirably raises the probability of extreme losses. Finally, we demonstrate that option prices in an economy with VaR risk managers display a volatility smile.

Suggested Citation

  • Arjan Berkelaar & Phornchanok Cumperayot & Roy Kouwenberg, 2002. "The Effect of VaR Based Risk Management on Asset Prices and the Volatility Smile," European Financial Management, European Financial Management Association, vol. 8(2), pages 139-164, June.
    • Handle: RePEc:bla:eufman:v:8:y:2002:i:2:p:139-164
    DOI: 10.1111/1468-036X.00182
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    Cited by:

    1. Cheridito, Patrick & Stadje, Mitja, 2009. "Time-inconsistency of VaR and time-consistent alternatives," Finance Research Letters, Elsevier, vol. 6(1), pages 40-46, March.
    2. Domenico Cuoco & Hua He & Sergei Isaenko, 2008. "Optimal Dynamic Trading Strategies with Risk Limits," Operations Research, INFORMS, vol. 56(2), pages 358-368, April.
    3. Chueh-Yung Tsao, 2010. "Portfolio selection based on the mean-VaR efficient frontier," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 931-945.
    4. Jose Arreola Hernandez & Sang Hoon Kang & Seong‐Min Yoon, 2022. "Nonlinear spillover and portfolio allocation characteristics of energy equity sectors: Evidence from the United States and Canada," Review of International Economics, Wiley Blackwell, vol. 30(1), pages 1-33, February.
    5. Wei Sun & Svetlozar Rachev & Frank J. Fabozzi, 2009. "A New Approach for Using Lévy Processes for Determining High‐Frequency Value‐at‐Risk Predictions," European Financial Management, European Financial Management Association, vol. 15(2), pages 340-361, March.
    6. Santiago Moreno-Bromberg & Traian Pirvu & Anthony R'eveillac, 2011. "CRRA Utility Maximization under Risk Constraints," Papers 1106.1702, arXiv.org, revised Mar 2012.
    7. Traian A. Pirvu & Gordan Žitković, 2009. "Maximizing The Growth Rate Under Risk Constraints," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 423-455, July.

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