A Fully Integrated Liquidity and Market Risk Model

Going beyond the simple bid–ask spread overlay for a particular value at risk, the author introduces an innovative framework that integrates liquidity risk, funding risk, and market risk. He overlaid a whole distribution of liquidity uncertainty on future market risk scenarios and allowed the liquidity uncertainty to vary from one scenario to another, depending on the liquidation or funding policy implemented. The result is one easy-to-interpret, easy-to-implement formula for the total liquidity-plus-market-risk profit and loss distribution.In this article, I introduce a new framework to integrate liquidity risk, funding risk, and market risk. The main result is a novel liquidity-plus-market-risk P&L distribution formula, which is easy to interpret and easy to implement. My approach improves on the current approaches to jointly modeling market risk and liquidity risk in seven ways:My liquidity model goes beyond a deterministic bid–ask spread overlay to a pure market risk component. Indeed, it models the full impact of any actual liquidation schedule, including impact uncertainty and impact correlations, as well as the differential impact between trading quickly and trading slowly.My liquidity model is state dependent: In those scenarios where the market is down and volatile, the adverse impact of any liquidation schedule is worse and, therefore, so is the liquidity of the portfolio.My liquidity model addresses both exogenous liquidity risk (arising from market conditions beyond our control) and funding risk (i.e., endogenous liquidity risk): Using this framework, one can model more aggressive liquidation schedules on capital-intensive securities specifically in those market scenarios that give rise to very negative P&L, all while no liquidation occurs in positive P&L scenarios.My liquidity model includes all the features of the market risk component beyond mean and variance. In particular, it models the P&L of not only nonsymmetrical tail events but also such nonlinear securities as complex derivatives.My liquidity model explicitly addresses the issue of estimation error, allowing for fast distributional stress testing via the fully flexible probabilities methodology (discussed later in the article).My methodology allows for a novel decomposition of risk into a market risk component and a liquidity risk component.My methodology also allows for a natural definition of the portfolio’s liquidity score in monetary units.From a methodology perspective, my approach relies on three pillars: (1) the literature on optimal execution—to model liquidity risk as a function of the actual trading involved; (2) an analytical conditional convolution—to blend market risk and liquidity/funding risk whereby different liquidation decisions are made in different market scenarios; and (3) the fully flexible probabilities approach—to model and stress test market risk even in highly non-normal portfolios with complex derivatives.My approach can be implemented efficiently with portfolios of thousands of securities, which can be accomplished by using the MATLAB code supporting the case study in the article (www.symmys.com/node/350).