Option pricing with an illiquid underlying asset market

    Authors

    H. Liu;J. M. Yong

    Comments

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    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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