Narrow Results

We construct a model for liquidity risk and price impacts in a limit order book setting with depth, resilience and tightness. We derive a wealth equation and a characterization of illiquidity costs. We show that we can separate liquidity costs due to depth and resilience from those related to tightness, and obtain a reduced model in which proportional costs due to the bid-ask spread is removed. From this, we obtain conditions under which the model is arbitrage free. By considering the standard utility maximization problem, this also allows us to obtain a stochastic discount factor and an asset pricing formula which is consistent with empirical findings (e.g., Brennan and Subrahmanyam (1996); Amihud and Mendelson (1986)). Furthermore, we show that in limiting cases for some parameters of the model, we derive many existing liquidity models present in the arbitrage pricing literature, including Çetin et al. (2004) and Rogers and Singh (2010). This offers a classification of different types of liquidity costs in terms of the depth and resilience of prices.

We consider a setup in which a large trader has sold a number of American-style derivatives and can have an impact on prices by trading the underlying asset for hedging purposes. The price impacts are assumed to be temporary and decay exponentially with time. Due to the impact of trading on prices, the large trader may also be tempted to minimize the payoff of the derivative by manipulating the underlying asset. Since the option holders have the right to exercise the option at any time before expiry, we consider a robust optimization problem for the large trader, in which the underlying uncertainty is the exercise time. It is shown that the solution of this optimization problem can be described as the solution of a double obstacle variational inequality. The optimal strategy for the large trader and the worst-case exercise time for the option holder are obtained explicitly in terms of the value function. We conclude with a sensitivity analysis in which we compare the timing and size of trades by the large trader as well as the exercise region for the options holders for different levels of liquidity, and identify situations that may lead to potential price manipulation.

This paper considers informed traders' trading strategy in a bear market. Known as stealth trading, informed traders use medium-size trades, which tend to contain more information than small and large trades, and have stronger impact on stock price movement. Using the transaction data provided by CSMAR database, we document the strong pattern of stealth trading in the Chinese stock market from June 1, 2004 to May 31, 2005, which is: (1) an order-driven market; (2) a market that has only limit orders; (3) a bear market; (4) a market with no corresponding derivative market and (5) a market with short-sale constraint. The empirical results add further evidence on stealth trading, in which informed traders tend to use medium-size trades, supported by the evidence that price movements are mainly due to medium-size trades. We find that the pattern in a bear market is highly consistent with that in a bull market. It is further documented that there is strong interaction between the stealth trading hypothesis and the order imbalance hypothesis, suggesting that the order imbalance effect should be considered when confirming the existence of stealth trading, or the levels of stealth trading.