Derivatives pricing with liquidity risk

• Author: Meryem Duygun,Yongmin Zhang,Shusheng Ding
• Date: 01 November 2019
• DOI: http://doi.org/10.1002/fut.22008
• Published date: 01 November 2019

Received: 23 December 2018

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Revised: 19 February 2019

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Accepted: 7 March 2019

DOI: 10.1002/fut.22008

RESEARCH ARTICLE

Derivatives pricing with liquidity risk

Yongmin Zhang

1

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Shusheng Ding

1

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Meryem Duygun

2

1

Department of Finance, School of

Business, Ningbo University, Ningbo,

China

2

Department of Finance, Nottingham

University Business School,

Nottingham, UK

Correspondence

Yongmin Zhang, School of Business,

Ningbo University, 818 Fenghua Road,

315211 Ningbo, China.

Email: zhangyongmin@nbu.edu.cn

Funding information

Ningbo‐CASS Collaborative grant, Grant/

Award Number: NZKT201701

Abstract

This paper develops a novel, general derivative pricing model which introduces

a liquidity risk factor. The model variants we outline offer a sufficient degree of

flexibility so as to enable the valuation of various types of derivative classes

including futures, American options, and mortgage backed security options,

whereas existing derivative models can only price liquidity risk in European

derivatives. We validate the model with oil and gold futures data and compare it

to a classical benchmark model void of any liquidity risk. We find that our

model is significantly more accurate than the classical model for pricing both oil

and gold contracts.

KEYWORDS

G13, derivative pricing, futures contracts, liquidity risk factor,

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INTRODUCTION

All securities suffer from liquidity risk. However, this particular source of risk is especially prevalent in less actively

traded securities, in light of the fact that price movements for less actively traded securities are typically more

pronounced on average. This study attempts to redress this deficiency by advancing a pricing model for derivative

securities that explicitly takes liquidity risk into account.

The impact of a liquidity risk factor on asset prices has received a large degree of attention in the field of financial

research. An abundance of asset pricing models incorporating an explicit liquidity factor have been developed, which

have mainly focused on equity markets, including the capital asset pricing model with liquidity, such as Acharya and

Pedersen (2005) and Liu (2006). By contrast, few existing studies incorporate liquidity measures developed specifically

for derivative markets. Only recently a number of studies have started paying closer attention to the impact of a

liquidity factor on derivative pricing, including those of Chou et al. (2011), Bongaerts, De Jong, and Driessen (2011), and

Feng, Hung, and Wang (2014). But these models are developed only for European‐style derivatives with restrictive

underlying asset classes such as stocks and simple‐structure bonds. The primary objective of this paper is to develop a

general model framework with the objective of pricing liquidity risk into various types of derivatives. These include

both European‐and American‐style derivatives with general underlying asset classes, such as mortgages, commodities,

real estate, and so forth. Mortgage backed securities (MBSs) have an embedded prepayment American option, and the

price of an MBS is equal to a price of a regular coupon bond with a fixed maturity minus the price of an American

option. Therefore, we argue that our newly proposed model is capable of pricing MBS products which are subject to

liquidity risk.

The significance of our novel contribution to the literature can be explained from multiple perspectives. First, based

on the existing literature, we set out to develop a derivative pricing model that incorporates a liquidity risk factor. The

model builds on the liquidity‐adjusted (LA) European option pricing model of Feng et al. (2014). However, Feng et al.

(2014) only utilize the estimated liquidity model parameters and not the liquidity level itself as inputs to improve the

standard Black–Scholes option pricing model. Owing to this particular approach, their model is only applicable to

J Futures Markets. 2019;39:1471–1485. wileyonlinelibrary.com/journal/fut © 2019 Wiley Periodicals, Inc.

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