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

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.

Keywords: value-at-risk, risk measure, price probability, market trades

JEL Classification: C10, E37, G11, G32