32 Pages Posted: 23 Feb 2013 Last revised: 1 Feb 2017
Date Written: January 1, 2007
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: 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
By Jim Gatheral