Bid-Ask Spread Formula and Liquidity Cost: Risk and Reward of a Market Maker
19 Pages Posted: 20 Jul 2000
Date Written: May 24, 2000
One of the fundamental properties of most markets is the existence of more than one asset price or distribution of prices for a given asset. In many markets this distribution is clearly bi-modal, and can be related to the so-called "bid" and "ask" positions. The underlying detailed "microscopic" kinetics of bids, offers, and their matches can be complex and includes information flow along with capital and inventory balances. The reduction of a micro-model to the observed bid-ask spread determines the parameters of interest. We study a dynamic modification of the Garman model without inventory shortages, and obtain a relationship between the bid-ask spread, Value-at-Risk of the market maker, required returns, and the rate of arrivals of orders (measure of liquidity). Our formula for the bid-ask spread can be parametrized by historical data and used as a key ingredient in the information systems and/or automatic trading systems. The formula is derived in the risk-premium pricing framework suggested earlier by one of us and Guo. The bid-ask spread and liquidity costs are computed theoretically and compared with estimates for the most traded equity stocks. The remainder of the paper explores the benefits of dynamic bid-ask trading strategies.
JEL Classification: G12, G14
Suggested Citation: Suggested Citation