Modeling Order-Flow Price Impact and Liquidity Risk in Nikkei Futures

Summary

This study develops a framework for relating order flow, price impact, and the market price of liquidity risk. Its analysis derives a differential equation and provides two closed-form solutions. One reproduces the linear order-flow impact associated with the classic informed-trader model; under less asymmetric information, the framework instead yields an S-shaped relationship between order flow and price impact.

The authors test the framework with intraday Nikkei futures data and compare its estimated impacts with industry heuristic functions. They argue that the model can estimate liquidity-risk parameters and offer a possible explanation for stochastic volatility and correlations. They also find that market depth reflects the market price of liquidity risk. The document does not report the sample period, quantitative fit, or execution costs, so it establishes a modeling perspective rather than enough evidence to assess practical trading performance.

Key ideas

• The framework connects order-flow price impact to the market price of liquidity risk.
• Its solutions include both a linear and an S-shaped impact curve.
• Intraday Nikkei futures data are used to estimate impact and compare it with industry heuristics.
• The model links liquidity-risk parameters with stochastic volatility and correlation.
• Market depth is found to encode information about the price of liquidity risk.

Tags

# Market Price of Trading Liquidity Risk and Market Depth


# Market Price of Trading Liquidity Risk and Market Depth









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.