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Pricing European Options in a Discrete Time Model for the Limit Order Book

Author

Listed:
  • Clarence Simard

    (Université du Québec à Montréal)

  • Bruno Rémillard

    (HEC Montreal)

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. We also deduce conditions to rule out arbitrage and solve the problem of pricing and hedging an European call option with physical delivery. It is shown that contrary to the perfectly liquid setting, the price of a European call is not given by an expectation, but can be expressed as an optimization problem on a set of equivalent probability measures.

Suggested Citation

  • Clarence Simard & Bruno Rémillard, 2019. "Pricing European Options in a Discrete Time Model for the Limit Order Book," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 985-1005, September.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:3:d:10.1007_s11009-017-9610-3
    DOI: 10.1007/s11009-017-9610-3
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    References listed on IDEAS

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    Cited by:

    1. Qi Guo & Anatoliy Swishchuk & Bruno R'emillard, 2022. "Multivariate Hawkes-based Models in LOB: European, Spread and Basket Option Pricing," Papers 2209.07621, arXiv.org.

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