Market Price of Trading Liquidity Risk and Market Depth

TL;DR

This paper introduces a new framework to analyze the market price of liquidity risk, deriving solutions that explain how order flow impacts prices and market depth, supported by empirical analysis of Nikkei futures.

Contribution

It develops a novel differential equation-based model for liquidity risk, providing closed-form solutions and linking market depth to liquidity risk pricing.

Findings

Derived two closed-form solutions for price impact.

Empirically validated the model using Nikkei futures data.

Showed market depth reflects the market price of liquidity risk.

Abstract

Price impact of a trade is an important element in pre-trade and post-trade analyses. We introduce a framework to analyze the market price of liquidity risk, which allows us to derive an inhomogeneous Bernoulli ordinary differential equation. We obtain two closed form solutions, one of which reproduces the linear function of the order flow in Kyle (1985) for informed traders. However, when traders are not as asymmetrically informed, an S-shape function of the order flow is obtained. We perform an empirical intra-day analysis on Nikkei futures to quantify the price impact of order flow and compare our results with industry's heuristic price impact functions. Our model of order flow yields a rich framework for not only to estimate the liquidity risk parameters, but also to provide a plausible cause of why volatility and correlation are stochastic in nature. Finally, we find that the market depth encapsulates the market price of liquidity risk.