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Non-Linear Value-at-Risk

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  • Mark Britten-Jones
  • Stephen M. Schaefer

Abstract

Value-at-risk methods which employ a linear ("delta only") approximation to the relation between instrument values and the underlying risk factors are unlikely to be robust when applied to portfolios containing non-linear contracts such as options. The most widely used alternative to the delta-only approach involves revaluing each contract for a large number of simulated values of the underlying factors. In this paper we explore an alternative approach which uses a quadratic approximation to the relation between asset values and the risk factors. This method (i) is likely to be better adapted than the linear method to the problem of assessing risk in portfolios containing non-linear assets, (ii) is less computationally intensive than simulation using full-revaluation and (iii) in common with the delta-only method, operates at the level of portfolio characteristics (deltas and gammas) rather than individual instruments.

Suggested Citation

  • Mark Britten-Jones & Stephen M. Schaefer, 1999. "Non-Linear Value-at-Risk," Review of Finance, European Finance Association, vol. 2(2), pages 161-187.
    • Handle: RePEc:oup:revfin:v:2:y:1999:i:2:p:161-187.
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    File URL: http://hdl.handle.net/10.1023/A:1009779322802
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    Cited by:

    1. Mozumder, Sharif & Dempsey, Michael & Kabir, M. Humayun & Choudhry, Taufiq, 2016. "An improved framework for approximating option prices with application to option portfolio hedging," Economic Modelling, Elsevier, vol. 59(C), pages 285-296.
    2. Zhu, Shushang & Zhu, Wei & Pei, Xi & Cui, Xueting, 2020. "Hedging crash risk in optimal portfolio selection," Journal of Banking & Finance, Elsevier, vol. 119(C).
    3. L. Jeff Hong & Sandeep Juneja & Guangwu Liu, 2017. "Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement," Operations Research, INFORMS, vol. 65(3), pages 657-673, June.
    4. Ortiz-Gracia, Luis, 2020. "Expected shortfall computation with multiple control variates," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    5. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, August.
    6. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    7. Castellacci, Giuseppe & Siclari, Michael J., 2003. "The practice of Delta-Gamma VaR: Implementing the quadratic portfolio model," European Journal of Operational Research, Elsevier, vol. 150(3), pages 529-545, November.
    8. Leitao, Álvaro & Oosterlee, Cornelis W. & Ortiz-Gracia, Luis & Bohte, Sander M., 2018. "On the data-driven COS method," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 68-84.
    9. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy, 2022. "Proper use of the modified Sharpe ratios in performance measurement: rearranging the Cornish Fisher expansion," Annals of Operations Research, Springer, vol. 313(2), pages 691-712, June.
    10. Seyed Mohammad Sina Seyfi & Azin Sharifi & Hamidreza Arian, 2020. "Portfolio Risk Measurement Using a Mixture Simulation Approach," Papers 2011.07994, arXiv.org.
    11. Manon Costa & Sébastien Gadat, 2021. "Non-asymptotic study of a recursive superquantile estimation algorithm," Post-Print hal-03610477, HAL.
    12. Gadat, Sébastien & Costa, Manon, 2020. "Non asymptotic controls on a stochastic algorithm for superquantile approximation," TSE Working Papers 20-1149, Toulouse School of Economics (TSE).
    13. Pang, Xiaochuan & Zhu, Shushang & Cui, Xueting & Ma, Jiali, 2023. "Systemic risk of optioned portfolio: Controllability and optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    14. Seyfi, Seyed Mohammad Sina & Sharifi, Azin & Arian, Hamidreza, 2021. "Portfolio Value-at-Risk and expected-shortfall using an efficient simulation approach based on Gaussian Mixture Model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1056-1079.
    15. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Estimating risks of option books using neural-SDE market models," Papers 2202.07148, arXiv.org.
    16. Chebbi, Ali & Hedhli, Amel, 2022. "Revisiting the accuracy of standard VaR methods for risk assessment: Using the Copula–EVT multidimensional approach for stock markets in the MENA region," The Quarterly Review of Economics and Finance, Elsevier, vol. 84(C), pages 430-445.
    17. Xiaochuan Pang & Shushang Zhu & Xueting Cui & Jiali Ma, 2022. "Systemic Risk of Optioned Portfolios: Controllability and Optimization," Papers 2209.04685, arXiv.org.
    18. Cortazar, Gonzalo & Beuermann, Diether & Bernales, Alejandro, 2013. "Risk Management with Thinly Traded Securities: Methodology and Implementation," IDB Publications (Working Papers) 4647, Inter-American Development Bank.

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