Option Pricing in a Discrete Time Model for the Limit Order Book

48 Pages Posted: 6 Aug 2014

See all articles by Clarence Simard

Clarence Simard

UQAM

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Date Written: July 26, 2014

Abstract

In this paper we build a discrete time model for the structure of the limit order book, so that the price per share depends on the size of the transaction. We deduce the value of a portfolio when the investor trades using market orders and a bank account with different interest rates for lending and borrowing. In this setting, we deduce conditions to rule out arbitrage and solve the problem of pricing and hedging an European call and put option with maturity one and physical delivery. By using primal-dual optimization we show that the price of European options can be written as an optimization problem over some set of probability measures.

Keywords: limit order book; discrete time; option pricing; non arbitrage

JEL Classification: C00, G13

Suggested Citation

Simard, Clarence and Remillard, Bruno, Option Pricing in a Discrete Time Model for the Limit Order Book (July 26, 2014). Available at SSRN: https://ssrn.com/abstract=2472410 or http://dx.doi.org/10.2139/ssrn.2472410

Clarence Simard (Contact Author)

UQAM ( email )

Montreal, Québec H3C 3P8
Canada

HOME PAGE: http://www.uqam.ca

Bruno Remillard

Department of Decision Sciences, HEC Montreal ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada
514-340-6794 (Phone)

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