Efficient price dynamics in a limit order market: an utility indifference approach

TL;DR

This paper develops a utility-based dynamic asset pricing model for limit order markets, capturing nonlinear prices, market impact, and optimal hedging, providing explicit formulas and insights into volatility and crashes.

Contribution

It introduces a novel utility indifference approach to model price dynamics with market impact and derives explicit efficient price representations.

Findings

Asset volatility depends on initial endowment convexity

Price crashes can be triggered by endowment shocks

Explicit efficient price formulas are provided for several cases

Abstract

We construct an utility-based dynamic asset pricing model for a limit order market. The price is nonlinear in volume and subject to market impact. We solve an optimal hedging problem under the market impact and derive the dynamics of the efficient price, that is, the asset price when a representative liquidity demander follows an optimal strategy. We show that a Pareto efficient allocation is achieved under a completeness condi- tion. We give an explicit representation of the efficient price for several examples. In particular, we observe that the volatility of the asset depends on the convexity of an initial endowment. Further, we observe that an asset price crash is invoked by an endowment shock. We establish a dynamic programming principle under an incomplete framework.