Abstract

We first investigate replication of a contingent claim in discrete time under liquidity risk. We model liquidity costs as a stochastic supply curve with an underlying asset price depending on order flow. We use a partial differential equation to define a delta-hedging strategy and show that the payoff of this discrete replicating strategy converges to the payoff of the option. We then investigate the utility indifference pricing to option valuation for a large trader in the market. We consider trading actions in illiquid markets will incur liquidity costs, but at the same time, the trader can have influence on the stock price evolution and gain benefits from the permanent price impact by choosing the optimal strategy. Thus, the option price, in some sense, is determined by these two contradicting phenomena.