IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2101.08559.html
   My bibliography  Save this paper

To VaR, or Not to VaR, That is the Question

Author

Listed:
  • Victor Olkhov

Abstract

We consider the core problems of the conventional value-at-risk (VaR) based on the price probability determined by frequencies of trades at a price p during an averaging time interval {\Delta}. To protect investors from risks of market price change, VaR should use price probability determined by the market trade time-series. To match the market stochasticity we introduce the new market-based price probability measure entirely determined by probabilities of random market time-series of the trade value and volume. The distinctions between the market-based and frequency-based price probabilities result different assessments of VaR and thus can cause excess losses. Predictions of the market-based price probability at horizon T equals the forecasts of the market trade value and volume probability measures.

Suggested Citation

  • Victor Olkhov, 2021. "To VaR, or Not to VaR, That is the Question," Papers 2101.08559, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:2101.08559
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2101.08559
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    2. Jeffery D. Amato & Eli M Remolona, 2005. "The pricing of unexpected credit losses," BIS Working Papers 190, Bank for International Settlements.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    4. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    5. Thomas J. Linsmeier & Neil D. Pearson, 1996. "Risk Measurement: An Introduction to Value at Risk," Finance 9609004, University Library of Munich, Germany.
    6. Victor Olkhov, 2020. "Price, Volatility and the Second-Order Economic Theory," Papers 2009.14278, arXiv.org, revised Apr 2021.
    7. David D. Friedman, 1990. "Price Theory: An Intermediate Text," Online economics textbooks, SUNY-Oswego, Department of Economics, number prin13.
    8. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    9. Olkhov, Victor, 2020. "Classical Option Pricing and Some Steps Further," MPRA Paper 105431, University Library of Munich, Germany, revised 28 Dec 2020.
    10. Victor Olkhov, 2020. "Volatility Depend on Market Trades and Macro Theory," Papers 2008.07907, arXiv.org.
    11. Olivier Gu'eant & Guillaume Royer, 2013. "VWAP execution and guaranteed VWAP," Papers 1306.2832, arXiv.org, revised May 2014.
    12. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Aramonte, Sirio & Giudice Rodriguez, Marius del & Wu, Jason, 2013. "Dynamic factor Value-at-Risk for large heteroskedastic portfolios," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4299-4309.
    15. E. Glen Weyl, 2019. "Price Theory," Journal of Economic Literature, American Economic Association, vol. 57(2), pages 329-384, June.
    16. Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 75, European Central Bank.
    17. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    18. Martin Auer, 2018. "Hands-On Value-at-Risk and Expected Shortfall," Management for Professionals, Springer, number 978-3-319-72320-4, December.
    19. Chaiyuth Padungsaksawasdi & Robert T. Daigler, 2018. "Volume weighted volatility: empirical evidence for a new realised volatility measure," International Journal of Banking, Accounting and Finance, Inderscience Enterprises Ltd, vol. 9(1), pages 61-87.
    20. Christopher Marshall & Michael Siegel, 1996. "Value at Risk: Implementing a Risk Measurement Standard," Center for Financial Institutions Working Papers 96-47, Wharton School Center for Financial Institutions, University of Pennsylvania.
    21. Francis X. Diebold (ed.), 2012. "Financial Risk Measurement and Management," Books, Edward Elgar Publishing, number 14102.
    22. Burton G. Malkiel, 1981. "Risk and Return: A New Look," NBER Working Papers 0700, National Bureau of Economic Research, Inc.
    23. R. L. Hall & C. J. Hitch, 1939. "Price Theory And Business Behaviour," Oxford Economic Papers, Oxford University Press, vol. 0(1), pages 12-45.
    24. Katerina Simons, 1996. "Value at risk: new approaches to risk management," New England Economic Review, Federal Reserve Bank of Boston, issue Sep, pages 3-13.
    25. Glyn A. Holton, 2002. "History of Value-at-Risk: 1922-1998," Method and Hist of Econ Thought 0207001, University Library of Munich, Germany.
    26. Linsmeier, Thomas J. & Pearson, Neil D., 1996. "Risk measurement: an introduction to value at risk," ACE Reports 14796, University of Illinois at Urbana-Champaign, Department of Agricultural and Consumer Economics.
    27. Berkowitz, Stephen A & Logue, Dennis E & Noser, Eugene A, Jr, 1988. " The Total Cost of Transactions on the NYSE," Journal of Finance, American Finance Association, vol. 43(1), pages 97-112, March.
    28. Enzo Busseti & Stephen Boyd, 2015. "Volume Weighted Average Price Optimal Execution," Papers 1509.08503, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Victor Olkhov, 2023. "Theoretical Economics as Successive Approximations of Statistical Moments," Papers 2310.05971, arXiv.org, revised Apr 2024.
    2. Victor Olkhov, 2021. "Three Remarks On Asset Pricing," Papers 2105.13903, arXiv.org, revised Jan 2024.
    3. Olkhov, Victor, 2022. "Introduction of the Market-Based Price Autocorrelation," MPRA Paper 112003, University Library of Munich, Germany.
    4. Olkhov, Victor, 2022. "The Market-Based Asset Price Probability," MPRA Paper 113096, University Library of Munich, Germany.
    5. Olkhov, Victor, 2022. "Economic Policy - the Forth Dimension of the Economic Theory," MPRA Paper 112685, University Library of Munich, Germany.
    6. Olkhov, Victor, 2023. "Economic Theory as Successive Approximations of Statistical Moments," MPRA Paper 118722, University Library of Munich, Germany.
    7. Olkhov, Victor, 2022. "Price and Payoff Autocorrelations in the Consumption-Based Asset Pricing Model," MPRA Paper 112255, University Library of Munich, Germany.
    8. Victor Olkhov, 2022. "Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics," Papers 2208.07839, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Victor Olkhov, 2021. "Three Remarks On Asset Pricing," Papers 2105.13903, arXiv.org, revised Jan 2024.
    2. Victor Olkhov, 2020. "Volatility Depend on Market Trades and Macro Theory," Papers 2008.07907, arXiv.org.
    3. Victor Olkhov, 2020. "Price, Volatility and the Second-Order Economic Theory," Papers 2009.14278, arXiv.org, revised Apr 2021.
    4. Victor Olkhov, 2022. "Market-Based Asset Price Probability," Papers 2205.07256, arXiv.org, revised Feb 2024.
    5. Olkhov, Victor, 2020. "Classical Option Pricing and Some Steps Further," MPRA Paper 105431, University Library of Munich, Germany, revised 28 Dec 2020.
    6. Vyacheslav Abramov & Fima Klebaner, 2007. "Estimation and Prediction of a Non-Constant Volatility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 1-23, March.
    7. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    8. Lars Stentoft, 2008. "Option Pricing using Realized Volatility," CREATES Research Papers 2008-13, Department of Economics and Business Economics, Aarhus University.
    9. Gonzalez-Rivera, Gloria & Lee, Tae-Hwy & Mishra, Santosh, 2004. "Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood," International Journal of Forecasting, Elsevier, vol. 20(4), pages 629-645.
    10. Marian Micu, 2005. "Extracting expectations from currency option prices: a comparison of methods," Computing in Economics and Finance 2005 226, Society for Computational Economics.
    11. Soohan Kim & Seok-Bae Yun & Hyeong-Ohk Bae & Muhyun Lee & Youngjoon Hong, 2022. "Physics-Informed Convolutional Transformer for Predicting Volatility Surface," Papers 2209.10771, arXiv.org, revised Nov 2023.
    12. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    13. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    14. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    15. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    16. Carvalho, Augusto & Guimaraes, Bernardo, 2018. "State-controlled companies and political risk: Evidence from the 2014 Brazilian election," Journal of Public Economics, Elsevier, vol. 159(C), pages 66-78.
    17. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    18. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    19. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    20. Rui Vilela Mendes & M. J. Oliveira, 2006. "A data-reconstructed fractional volatility model," Papers math/0602013, arXiv.org, revised Jun 2007.

    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G1 - Financial Economics - - General Financial Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2101.08559. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.