Market liquidity risk refers to the degree to which large size transactions can be carried out in a timely fashion with minimal impact on prices. Emphasized by the G10 report in 1993 and the BIS report in 1997, it is one factor of destabilization in the financial markets, as illustrated recently by the Asian crisis, the failure of the hedge fund LTCM during the Russian crisis. So in order to assess welfare implications of portfolio insurance strategies, it would be to estimate the dynamic hedging activity in securities markets through a specific parsimonious and realistic model. In the paper, large traders hold sufficient liquid assets to meet liquidity needs of other traders, and so bear the risk of their imbalanced derivatives portfolio. As a result of their dynamic hedging strategies, through endogenous non-linear positive feedback effects, they buy and sell derivatives at prices shifted by an amount that depends on their net holding. We show how dynamic hedging may directly and endogenously give rise to empirically observed bid-offer spreads, of which we then analyse the two main underlying factors: inventory holding costs and informational asymmetry, thus requiring specific strategic trades in order to tackle portfolio insurance strategy paradox. More specifically we offer partial hedging strategies, such as “feedback volatility” pricing and state-dependent threshold value strategies, illustrating a trade-off between maximizing expected gains and minimizing mis-hedging risk. Moreover we also discuss delicate positions’ gamma hedging, which requires creating vega positions in order to profit from the "feedback" volatility, in both long and short term. Finally we model the information asymmetry linked to the specific structure of the options portfolio and devise intertemporal arbitrage strategies for the large player.
