A Fully Integrated Liquidity Market Risk Model

We overlay a whole distribution of liquidity uncertainty on future market risk scenarios and we allow 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. Using this formula we can stress-test different market risk P&L distributions and different scenario-dependent liquidation policies and funding policies; compute total risk and decompose it into a novel liquidity-plus-market risk formula; and define a liquidity score as a monetary measure of portfolio liquidity. Our approach relies on three pillars: first, the literature on optimal execution, to model liquidity risk as a function of the actual trading involved; second, an analytical conditional convolution, to blend market risk and liquidity/funding risk; third the Fully Flexible Probabilities framework, to model and stress-test market risk even in highly non-normal portfolios with complex derivatives. Our approach can be implemented efficiently with portfolios of thousand of securities. The code for the case study is available at http://www.symmys.com/node/350.