Financial Markets and Trading: An Introduction to Market Microstructure and Trading Strategies

CHAPTER 3

Inventory Models

It was indicated in Chapter 1 that market makers in dealers’ markets provide liquidity for takers and make money from the bid/ask spread. This seems easy, particularly in the case of a single-dealer platform. However, there is always a danger that the buy order flows and the sell order flows are not balanced. For example, if there is selling pressure, the price decreases. Then the dealer (who has an obligation to maintain inventory) may have to sell an asset at a price lower than the price at which he bought the asset some time ago. In the long run, the price may revert, but the problem is that the dealer with limited cash resources can become broke before restoring his inventory.

In this chapter, I discuss the models that address the market maker's risk of maintaining inventory as well as show how the size of the bid/ask spread can compensate this risk. Various inventory models differ in whether they account for risk aversion explicitly. I start with the implicit (risk-neutral) models offered by Garman (1976), and Amihud & Mendelson (1980). Then I introduce a formalized notion of risk aversion and describe the explicit Stoll's model (1978).

RISK-NEUTRAL MODELS

The Garman's Model

The problem of dealer's inventory imbalance was first addressed by Garman (1976). In his model, a monopolistic dealer assigns ask (p_a) and bid (p_b) prices, and fills all orders. Each order size is assumed to be one unit. The dealer's goal is, as a minimum, to avoid bankruptcy ...