Liquidity Stress Testing using Optimal Portfolio Liquidation

We build an optimal portfolio liquidation model for OTC markets, aiming at minimizing the trading costs via the choice of the liquidation time. We work in the Locally Linear Order Book framework of \cite{toth2011anomalous} to obtain the market impact as a function of the traded volume. We find that the optimal terminal time for a linear execution of a small order is proportional to the square root of the ratio between the amount being bought or sold and the average daily volume. Numerical experiments on real market data illustrate the method on a portfolio of corporate bonds.