Title

The modeling of liquidity in the value-at-risk framework

Date of Completion

January 2001

Keywords

Economics, Finance|Economics, Theory|Business Administration, Banking

Degree

Ph.D.

Abstract

This dissertation is an exposition of a new method of modeling liquidity in the Value-at-Risk (VaR) framework. Liquidity, in general, refers to the deviation of transaction price from the intrinsic value of a security. Prior research has focused on the size of that deviation defined as the bid-ask spread set by the dealer to compensate him for adverse selection and inventory costs. Instead, the model proposed here looks at the time it takes to liquidate a position in the market and its relationship to the VaR of the agent's portfolio. This has not been done before. ^ The dissertation is divided as follows. Chapter 1 contains a critique of the VaR modeling literature from an implementation perspective of a financial institution. It provides a motivation for a liquidity adjustment model which is independent of the probability assumption for the underlying risk factors and the composition of the agent's portfolio, and, specifically, whether it contains any non-linear assets (e.g. convex bonds and options). Numerical examples show that the inclusion of derivatives in the portfolio renders many specialized approximate methods inadequate. Chapter 2 develops a theoretical framework for the inclusion of the time dimension of liquidity into the VaR framework, irrespective of whether the sources of liquidity are exogenous (beyond the institution's control) or endogenous (related to the size of the institution's portfolio relative to the market depth). It proposes a statistical aggregation procedure which relies on conditional multivariate sampling to account for the case where liquidity is constrained by a slow speed of trading in a given market. Chapter 3 investigates the optimal behavior of an agent faced with selling his holdings, which may be large relative to the size of the entire market. He solves for the liquidation horizon that represents the best tradeoff between the volatility of the stochastic process for the equilibrium return and a depressed price due to the liquidation program's market impact. The impact specifications are either general power or linear functions correlated with the underlying returns. They allow for the empirically observed phenomenon of liquidity shocks appearing during rapid market price compressions. ^