# Optimal VWAP execution under transient price impact

## TL;DR

This paper derives explicit solutions for optimal VWAP trading strategies considering linear, transient market impact, extending previous models to more general trading intervals and revealing that optimal strategies can involve both buying and selling.

## Contribution

It introduces a comprehensive model for optimal VWAP execution with transient impact, encompassing various benchmark cases and providing explicit solutions for risk-averse investors.

## Key findings

- Explicit solutions for continuous and discrete time models.
- Optimal strategies may involve both buying and selling.
- Contrasts with Implementation Shortfall where only one direction is optimal.

## Abstract

We solve the problem of optimal liquidation with volume weighted average price (VWAP) benchmark when the market impact is linear and transient. Our setting is indeed more general as it considers the case when the trading interval is not necessarily coincident with the benchmark interval: Implementation Shortfall and Target Close execution are shown to be particular cases of our setting. We find explicit solutions in continuous and discrete time considering risk averse investors having a CARA utility function. Finally, we show that, contrary to what is observed for Implementation Shortfall, the optimal VWAP solution contains both buy and sell trades also when the decay kernel is convex.