A parabolic variational inequality arising from the valuation of strike reset options

Zhou Yang; Fahuai Yi; Min Dai

doi:10.1016/j.jde.2006.07.026

A parabolic variational inequality arising from the valuation of strike reset options

Zhou Yang, Fahuai Yi, Min Dai

Department of Applied Mathematics

Research output: Journal article publication › Journal article › Academic research › peer-review

8 Citations (Scopus)

Abstract

A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C^∞ smoothness of the free boundary are proven in some situations.

Original language	English
Pages (from-to)	481-501
Number of pages	21
Journal	Journal of Differential Equations
Volume	230
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2006.07.026
Publication status	Published - 15 Nov 2006

Keywords

American option
Free boundary
Option pricing
Strike reset option
Variational inequality

ASJC Scopus subject areas

Analysis
Applied Mathematics

More information

10.1016/j.jde.2006.07.026

Cite this

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abstract = "A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C∞ smoothness of the free boundary are proven in some situations.",

keywords = "American option, Free boundary, Option pricing, Strike reset option, Variational inequality",

author = "Zhou Yang and Fahuai Yi and Min Dai",

note = "Funding Information: ✩ The project supported by National Natural Science Foundation of China (No. 10371045, No. 10426015 and No. 10301002) and NSF of Guangdong province (No. 5005930). * Corresponding author. E-mail address: [email protected] (F. Yi).",

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AB - A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C∞ smoothness of the free boundary are proven in some situations.

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A parabolic variational inequality arising from the valuation of strike reset options

Abstract

Keywords

ASJC Scopus subject areas

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