The cost of illiquidity and its effects on hedging

After credit risk, liquidity risk is probably the next most important risk faced by the finance industry; and yet the study of liquidity is far less advanced. This may be in part due to the fact that there is no agreed definition of what liquidity is, even in qualitative terms; everyone would agree that the effect of illiquidity is to make it difficult or costly to trade large volumes of the underlying asset in small times, but there are different approaches to modelling this. One modelling philosophy is that trading large amounts moves the price, and the papers of [7], [8], [16], [15], [18] are examples of this viewpoint, where the stock price responds instantaneously to the amount of the stock held by a single large trader. Though such models have a flavour of liquidity, we regard them rather as models of price impact effects. There is evidence that the actions of a large trader can influence the price of the underlying (see, for example, [12] and [10] ). A large trader can try to ‘corner the market’. One way to do this in a commodity market is to take a huge long futures position and at the same time buy up the underlying commodity. As expiry approaches the investors who are short the futures contract may find that there is not enough supply to meet their demand and hence the price is pushed up. One such alleged case of this was the activities of the Hunt brothers in the silver market in 1979-1980. Their trading caused the price to increase from $9 per ounce to $50 per ounce. Another way to ‘corner the market’, this time involving shares, is to buy up a large supply and then lend some to investors who want to go short. When these shares are sold on the market the agent buys them up and then calls in the short shares. Since the agent has limited the supply of shares by buying a large amount, this pushes the price up. These types of manipulation involve taking huge positions in the underlying and documented examples of this type of activity have shown large price increases followed by a crash. Though interesting in their own right, such price impact models have drawbacks which make them unsuitable as models of liquidity. One of these is the ‘free round trip’ phenomenon, discussed in [18]; if the large agent rapidly sells and then buys back a large amount of stock, he can force the price instantaneously to drop, and if this round trip is not costly (as is the case in some studies), then the large agent could make profits by selling down-and-out calls,