Liquidity Risk Estimation Using Fuzzy Measure Theory

One of the most relevant issues in the risk analysis of the financial institutions´ investments is to determine the capital allocation in order to maintain its solvency and liquidity in adverse situations. The portfolio risk analysis is necessary for assuring the right selection of that capital to be allocated. Each portfolio has a market risk. This risk is directly related to the losses that can be caused by adverse fluctuations of the portfolio asset prices. In this sense, it is necessary to construct a measure able to quantify the potential losses associated with that exposure. The classical Value-at-Risk measures the pure market risk; therefore, it does not bear some considerations. If a financial institution uses this classical framework to determine the quantity of capital to allocate in order to face its obligations with a certain level of confidence, then the institution does not take into account the partial or total portfolio liquidation consequences at the claim moment. To take into account these consequences is crucial because the number of assets to be sold in the market has an important influence in the price at which the transaction will be made. This influence is determined by the market liquidity at that moment. When these problems take place the financial institution could have liquidity problems to cancel its obligations. This paper develops and applies a Value-at-Risk model regarding prices fluctuations and potential market liquidity problems. Due to uncertainty of market liquidity in the future, the model includes Fuzzy Measure Theory . The first section of the paper presents some fundamental concepts of Fuzzy Measure Theory and Extreme Value Theory . The second section presents a “fuzzified” risk valuation model under the classical assumption of normal distribution for the investment returns; and, taking into consideration the Argentinean financial crisis, also presents the model under an Extreme Value Theory distribution. Both alternatives are applied to a portfolio of Repsol-YPF stocks so as to estimate the risk assumed by the holder.