Title

Option Pricing With An Illiquid Underlying Asset Market

Keywords

Illiquidity; Option pricing; Price impact; Volatility smile

Abstract

We examine how price impact in the underlying asset market affects the replication of a European contingent claim. We obtain a generalized Black-Scholes pricing PDE and establish the existence and uniqueness of a classical solution to this PDE. Unlike the case with transaction costs, we prove that replication with price impact is always cheaper than superreplication. Compared to the Black-Scholes case, a trader generally buys more stock and borrows more (shorts and lends more) to replicate a call (put). Furthermore, price impact implies endogenous stochastic volatility and an out-of-money option has lower implied volatility than an in-the-money option. This finding has important implications for empirical analysis on volatility smile. © 2005 Elsevier B.V. All rights reserved.

Publication Date

12-1-2005

Publication Title

Journal of Economic Dynamics and Control

Volume

29

Issue

12

Number of Pages

2125-2156

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jedc.2004.11.004

Socpus ID

28044439577 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/28044439577

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