Option prices under liquidity risk as weak solutions of semilinear diffusion equations

Matthias Albrecht Fahrenwaldt; Alexandre F. Roch

doi:10.1007/s00030-017-0435-0

Option prices under liquidity risk as weak solutions of semilinear diffusion equations

Matthias Albrecht Fahrenwaldt, Alexandre F. Roch

Research output: Contribution to journal › Article › peer-review

73 Downloads (Pure)

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.

Original language	English
Article number	12
Number of pages	32
Journal	Nonlinear Differential Equations and Applications
Volume	24
Issue number	2
Early online date	18 Feb 2017
DOIs	https://doi.org/10.1007/s00030-017-0435-0
Publication status	Published - Apr 2017

Access to Document

10.1007/s00030-017-0435-0Licence: CC BY

Download pdf
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Final published version, 723 KBLicence: CC BY

Cite this

@article{46d8d80b688d4ae080f59cc4b803be95,

title = "Option prices under liquidity risk as weak solutions of semilinear diffusion equations",

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.",

author = "Fahrenwaldt, {Matthias Albrecht} and Roch, {Alexandre F.}",

year = "2017",

month = apr,

doi = "10.1007/s00030-017-0435-0",

language = "English",

volume = "24",

journal = "Nonlinear Differential Equations and Applications",

issn = "1021-9722",

publisher = "Birkh{\"a}user",

number = "2",

}

TY - JOUR

T1 - Option prices under liquidity risk as weak solutions of semilinear diffusion equations

AU - Fahrenwaldt, Matthias Albrecht

AU - Roch, Alexandre F.

PY - 2017/4

Y1 - 2017/4

N2 - 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.

AB - 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.

U2 - 10.1007/s00030-017-0435-0

DO - 10.1007/s00030-017-0435-0

M3 - Article

SN - 1021-9722

VL - 24

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 2

M1 - 12

ER -

Option prices under liquidity risk as weak solutions of semilinear diffusion equations

Abstract

Access to Document

Fingerprint

Cite this