Narrow Results

We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a tradeoff between minimizing the risk against fluctuations in the stock price and incurring low liquidity costs. We work in an arbitrage-free setting assuming a supply curve for each asset. In discrete time, we prove the existence of a locally risk-minimizing strategy under mild conditions on the price process. Under stochastic and time-dependent liquidity risk we give a closed-form solution for an optimal strategy in the case of a linear supply curve model. Finally we show how our hedging method can be applied in energy markets where futures with different maturities are available for trading. The futures closest to their delivery period are usually the most liquid but depending on the contingent claim not necessarily optimal in terms of hedging. In a simulation study, we investigate this tradeoff and compare the resulting hedge strategies with the classical ones.

We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon T. A trader uses both limit and market orders, and a large market order faces an adverse price movement caused by the liquidity risk. First, we study a single period model where the trader places a limit order and/or a market order at the beginning. We show the behavior of optimal amount of market order, $m^{*}$, and optimal placement of limit order, $y^{*}$, under different market conditions. Next, we extend it to a multi-period model, where the trader makes sequential decisions of limit and market orders at multiple time points.