Optimal Liquidation in a Defaultable Market

TL;DR

This paper develops an explicit solution for the optimal liquidation strategy of a large portfolio of defaultable securities, considering market impact and default risk modeled via a Brownian motion.

Contribution

It provides a novel explicit solution to the optimal liquidation problem in a defaultable market with market impact, extending existing models.

Findings

Explicit formula for the value function

Characterization of the optimal liquidation strategy

Quantitative insights into market impact effects

Abstract

In this paper we address the problem of optimal liquidation of a large portfolio composed by securities exposed to default risk. The default time is described in terms of a Brownian motion representing the evolution of the value of the firm, whose assets are available in the market for investors. Considering that selling a large number of assets has a significant impact in the price, and hence in the portfolio's value, the control problem involved to describe the optimal strategy to liquidate a large position is analyzed. Under suitable assumptions in the model, an explicit solution is given to the value function and a precise description of the optimal strategy is obtained.