Option Prices under Liquidity Risk as Weak Solutions of Semilinear Diffusion Equation

32 Pages Posted: 23 Feb 2013 Last revised: 1 Feb 2017

Matthias Fahrenwaldt

EBZ Business School; Leibniz Universität Hannover

Alexandre F. Roch

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG)

Date Written: January 1, 2007

Abstract

Prices of financial options in a market with liquidity risk are shown to be weak solutions of a class of semilinear parabolic partial differential equations with nonnegative characteristic form. We prove the existence and uniqueness of such solutions, and then show the solutions correspond to option prices as defined in terms of replication in a probabilistic setup. We obtain an asymptotic representation of the price and the hedging strategy as a liquidity parameter converges to zero.

Keywords: Liquidity risk, Option pricing, Semilinear degenerate parabolic partial differential equations, Nonlinear analysis

JEL Classification: C60, D40, G13

Suggested Citation

Fahrenwaldt, Matthias and Roch, Alexandre F., Option Prices under Liquidity Risk as Weak Solutions of Semilinear Diffusion Equation (January 1, 2007). Available at SSRN: https://ssrn.com/abstract=2222769 or http://dx.doi.org/10.2139/ssrn.2222769

Matthias Fahrenwaldt

EBZ Business School ( email )

Springorumallee 20
Bochum, 44795
Germany

Leibniz Universität Hannover

Institut für Mathematische Stochastik
Welfengarten 1
30167 Hannover, DE 30167
Germany

Alexandre F. Roch (Contact Author)

University of Quebec at Montreal (UQAM) - Faculty of Management (ESG) ( email )

Case postale 8888
Succursale Centre-ville
Montreal, Quebec H3C 3P8
Canada

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