Hedge and Speculate: Replicating Option Payoffs with Limit and Market Orders

We show how to execute a basket consisting of a subset of co-moving assets and demonstrate how the information carried in other traded assets, which are not in the basket, improves execution performance. Market orders (MOs) from all participants, including the agent's orders to execute her basket, have permanent price impact on the assets, i.e. executions in a single asset affect prices of all assets. Furthermore, we assume the agent's MOs are executed at worse than midprices (by walking the LOB) through a temporary price impact. The execution problem is posed as an optimal stochastic control one and we reduce the dynamic programming equation to a system of coupled partial differential equations, which reduces to a coupled system of Riccati equations when other agents' order flow are deterministic. We use data of five stocks traded in the Nasdaq exchange to estimate the model parameters and use simulations to illustrate the performance of the strategy. As an example, the agent liquidates a portfolio consisting of shares in INTC and SMH. We show that including the information provided by three additional assets (FARO, NTAP, ORCL) considerably improves the strategy's performance -- for the portfolio we execute, it outperforms the multi-asset version of Almgren-Chriss by approximately 2 to 4 basis points per share.