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

30 Pages Posted: 13 Apr 2017

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Luhui Gan

University of Toronto

Sebastian Jaimungal

University of Toronto - Department of Statistics

Date Written: April 12, 2017

Abstract

We consider an agent who takes a short position in a contingent claim and employs limit orders (LOs) and market orders (MOs) to trade in the underlying asset to maximize expected utility of terminal wealth. The agent solves a combined optimal stopping and control problem where trading has frictions: MOs (executed by the agent and other traders) have permanent price impact and pay exchange fees, and LOs earn the spread (relative to the midprice of the asset) and pay no exchange fees. We show how the agent replicates the payoff of the claim and also speculates in the asset to maximize expected utility of terminal wealth. In the strategy, MOs are used to keep the inventory on target, to replicate the payoff, and LOs are employed to build the inventory at favorable prices and boost expected terminal wealth by executing roundtrip trades that earn the spread. We calibrate the model to the E-mini contract that tracks the S&P500 index, provide numerical examples of the performance of the strategy, and proof the convergence of the numerical scheme we employ.

Keywords: Optimal hedging, market impact, impulse control, algorithmic trading, high-frequency trading

JEL Classification: C6, C61, D81, G1, G13

Suggested Citation

Cartea, Álvaro and Gan, Luhui and Jaimungal, Sebastian, Hedge and Speculate: Replicating Option Payoffs with Limit and Market Orders (April 12, 2017). Available at SSRN: https://ssrn.com/abstract=2952132 or http://dx.doi.org/10.2139/ssrn.2952132

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Luhui Gan

University of Toronto ( email )

Toronto, Ontario M5S 3G8
Canada

Sebastian Jaimungal (Contact Author)

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
343
Abstract Views
1,240
rank
95,638
PlumX Metrics