Title

Option pricing with an illiquid underlying asset market

Authors

Authors

H. Liu;J. M. Yong

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

J. Econ. Dyn. Control

Keywords

price impact; option pricing; illiquidity; volatility smile; CONSUMPTION CHOICES; TRANSACTION COSTS; MANIPULATION; PORTFOLIO; VOLATILITY; Economics

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, it trader generally buys more Stock and borrows more (shorts and ends more) to replicate a call (put). furthermore, price impact implies endogenous stochastic volatility and all out-of-money option has lower implied volatility than in in-the-money option. This finding has important implications for empirical analysis on volatility smile. (c) 2005 Elsevier B.V. All rights reserved.

Journal Title

Journal of Economic Dynamics & Control

Volume

29

Issue/Number

12

Publication Date

1-1-2005

Document Type

Article

Language

English

First Page

2125

Last Page

2156

WOS Identifier

WOS:000233764100002

ISSN

0165-1889

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