Olkhov, Victor (2021): To VaR, or Not to VaR, That is the Question.

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Abstract
This paper discusses the valueatrisk (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 nth statistical moments as ratio of nth 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.
Item Type:  MPRA Paper 

Original Title:  To VaR, or Not to VaR, That is the Question 
English Title:  To VaR, or Not to VaR, That is the Question 
Language:  English 
Keywords:  valueatrisk; risk measure; price probability; market trades 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods D  Microeconomics > D4  Market Structure, Pricing, and Design > D46  Value Theory D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty G  Financial Economics > G1  General Financial Markets G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates G  Financial Economics > G1  General Financial Markets > G17  Financial Forecasting and Simulation 
Item ID:  105458 
Depositing User:  Victor Olkhov 
Date Deposited:  25 Jan 2021 02:51 
Last Modified:  25 Jan 2021 02:51 
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Jour. of Derivatives, 1(1),7184 DOI: https://doi.org/10.3905/jod.1993.407868 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/105458 