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

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  • Olkhov, Victor

Abstract

This paper discusses the value-at-risk (VaR) concept and assesses the financial adequacy of the price probability determined by frequency of trades at price p. We take the price definition as the ratio of executed trade value to volume and show that it leads to price statistical moments, which differ from those, generated by frequency price probability. We derive the price n-th statistical moments as ratio of n-th statistical moments of the value and the volume of executed transactions. We state that the price probability determined by frequency of trades at price p doesn’t describe probability of executed trade prices and VaR based on frequency price probability may be origin of unexpected and excessive losses. We explain the need to replace frequency price probability by frequency probabilities of the value and the volume of executed transactions and derive price characteristic function. After 50 years of the VaR usage main problems of the VaR concept are still open. We believe that VaR commitment to forecast the price probability for the time horizon T seems to be one of the most tough and expensive puzzle of modern finance.

Suggested Citation

  • Olkhov, Victor, 2021. "To VaR, or Not to VaR, That is the Question," MPRA Paper 105458, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:105458
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    Cited by:

    1. Victor Olkhov, 2021. "Three Remarks On Asset Pricing," Papers 2105.13903, arXiv.org, revised Jan 2024.
    2. Victor Olkhov, 2022. "Market-Based Asset Price Probability," Papers 2205.07256, arXiv.org, revised Feb 2024.
    3. Olkhov, Victor, 2022. "Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics," MPRA Paper 114187, University Library of Munich, Germany.
    4. Victor Olkhov, 2023. "Theoretical Economics as Successive Approximations of Statistical Moments," Papers 2310.05971, arXiv.org, revised Apr 2024.
    5. Olkhov, Victor, 2022. "Introduction of the Market-Based Price Autocorrelation," MPRA Paper 112003, University Library of Munich, Germany.
    6. Olkhov, Victor, 2022. "Economic Policy - the Forth Dimension of the Economic Theory," MPRA Paper 112685, 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. Olkhov, Victor, 2023. "Economic Theory as Successive Approximations of Statistical Moments," MPRA Paper 118722, University Library of Munich, Germany.

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    More about this item

    Keywords

    value-at-risk; risk measure; price probability; market trades;
    All these keywords.

    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

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