The pricing of average options with jump diffusion processes in the uncertain volatility model

Yulian Fan and Huadong Zhang
Additional contact information
Yulian Fan: School of Science, North China University of Technology, Beijing 100144, China
Huadong Zhang: School of Science, North China University of Technology, Beijing 100144, China

International Journal of Financial Engineering (IJFE), 2017, vol. 04, issue 01, 1-31

Abstract: The pricing equations of the average options with jump diffusion processes can be formulated as two-dimensional partial integro-differential equations (PIDEs). In the uncertain volatility model, for options with non-convex and non-concave payoffs, such as the butterfly spread, the PIDEs are nonlinear. We use the semi-Lagrangian method to reduce the two-dimensional nonlinear PIDE to a one-dimensional nonlinear PIDE along the trajectory of the average price, and use a Newton-type iteration to guarantee the convergence of the discrete solution to the viscosity solution. Monotonicity and stability as well as the convergence results are derived. Numerical tests of convergence for a variety of cases, including average butterfly spread and ordinary butterfly spread, are presented.

Keywords: Uncertain volatility; average butterfly spread; semi-Lagrangian; jump diffusion (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S2424786317500050
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijfexx:v:04:y:2017:i:01:n:s2424786317500050

Ordering information: This journal article can be ordered from

DOI: 10.1142/S2424786317500050

Access Statistics for this article

International Journal of Financial Engineering (IJFE) is currently edited by George Yuan

More articles in International Journal of Financial Engineering (IJFE) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().