Pricing Liquidity: The Quantity Structure of Immediacy Prices

by George C. Chacko, Jakub W. Jurek & Erik Stafford

Overview — Researchers and participants in the market for securities have long been interested in the costs of transacting and the notion of liquidity as a performance measure of market structure. In real world capital markets, investors and corporations generally do not expect to transact at fundamental value. Rather, market participants face some degree of illiquidity, where they must sacrifice price, trade size, or speed of execution, forcing them to transact at prices away from fundamental value. The exact price of liquidity, however, is unknown. This paper develops an option-based model of the price of liquidity via the pricing of limit orders. Key concepts include:

The model points to the competitiveness of market making as a potentially important driver of transaction prices.
The model results in a simple formula that can be used to estimate transaction prices as a function of transaction size for individual securities, including very large transactions like corporate issues and takeovers.
The uncertainty over transactable prices, relative to fundamental value, produces a liquidity risk. The model may be a useful step towards a new measure of liquidity risk.

Author Abstract

This paper develops a model for understanding liquidity via the pricing of limit orders. Limit orders can be well defined and priced with the tools of option pricing, allowing the complex tradeoff between transaction size and speed to be reduced to a single price. The option-based framework allows the properties of liquidity to be characterized as functions of the fundamental value and the order flow processes. In the special case when immediate execution is desired, the option strike price at which immediate exercise is optimal determines the effective bid/ask price. A model with full-information, but imperfect market making, is able to describe many of the known properties of transaction costs.