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Tradable measure of risk

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Author Info
Pospisil, Libor
Vecer, Jan
Xu, Mingxin

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Abstract

The main idea of this paper is to introduce Tradeable Measures of Risk as an objective and model independent way of measuring risk. The present methods of risk measurement, such as the standard Value-at-Risk supported by BASEL II, are based on subjective assumptions of future returns. Therefore two different models applied to the same portfolio can lead to different values of a risk measure. In order to achieve an objective measurement of risk, we introduce a concept of {\em Realized Risk} which we define as a directly observable function of realized returns. Predictive assessment of the future risk is given by {\em Tradeable Measure of Risk} -- the price of a financial contract which pays its holder the Realized Risk for a certain period. Our definition of the Realized Risk payoff involves a Weighted Average of Ordered Returns, with the following special cases: the worst return, the empirical Value-at-Risk, and the empirical mean shortfall. When Tradeable Measures of Risk of this type are priced and quoted by the market (even of an experimental type), one does not need a model to calculate values of a risk measure since it will be observed directly from the market. We use an option pricing approach to obtain dynamic pricing formulas for these contracts, where we make an assumption about the distribution of the returns. We also discuss the connection between Tradeable Measures of Risk and the axiomatic definition of Coherent Measures of Risk.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5059.

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Date of creation: 27 Sep 2007
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Handle: RePEc:pra:mprapa:5059

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Related research
Keywords: dynamic risk measure conditional value-at-risk shortfall

Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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