Liquidity Modelling and Optimal Liquidation in Bond Markets

The focus of this paper is on the modelling of defaultable bonds and the optimal liquidation of portfolios of such bonds. By developing an existing credit intensity model, we suggest a framework for valuing defaultable bonds that allows for capturing, not only the default risk, but also the liquidity risk. We investigate empirically defaultable bonds and extract their liquidity risk within this model. We observe a regime shift at the beginning of the credit crisis in the liquidity risk of a range of defaultable bonds. The third part of the paper is on optimal liquidation of portfolios of defaultable bonds. The portfolio liquidation problem for bonds can be formulated as a multiple optimal stopping problem, where stopping corresponds to the sale of a certain quantity of the asset. We allow the depth of the market to depend on the liquidity yield of each bond and for sales to put a downward pressure on the price depending on the size of the trade. We then show the relative effect of the change in liquidity over the credit crisis in the amount that a bond portfolio can be liquidated for under this model.