Fully Integrated Liquidity and Market Risk Model

We introduce a new framework to integrate liquidity risk, funding risk and market risk, which goes beyond the simple bid-ask spread overlay to a VaR number. In our approach, we overlay a whole distribution of liquidity uncertainty to each future market-risk scenario. Then we allow for the liquidity uncertainty to vary scenario by scenario, depending on what liquidation policy or funding policy is implemented in that scenario. The result is one easy-to-interpret and easy-to-implement formula for the total liquidity-plus-market-risk P&L 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 for download