Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model

Xiaoying Jiang, Chunmei Shi () and Yujie Wei
Additional contact information
Xiaoying Jiang: School of Mathematics and Computer Science, Zhejiang A&F University, Hangzhou 311300, China
Chunmei Shi: School of Mathematics and Computer Science, Zhejiang A&F University, Hangzhou 311300, China
Yujie Wei: School of Mathematics Sciences, Zhejiang University, Hangzhou 310027, China

Mathematics, 2025, vol. 13, issue 15, 1-14

Abstract: In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to solve the initial boundary value problem. The latter aims to recover the implied volatility via observable option prices. Using a linearization technique, we rigorously derive a mathematical formulation of the inverse problem in terms of a Fredholm integral equation of the first kind. Based on an integral equation, an efficient numerical reconstruction algorithm is proposed to recover the coefficient. Numerical results for both problems are provided to illustrate the validity and effectiveness of proposed methods.

Keywords: spatial-fractional Black–Scholes equation; CN-WSGD scheme; linearization technique; reconstruction algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/15/2480/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/15/2480/ (text/html)

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:gam:jmathe:v:13:y:2025:i:15:p:2480-:d:1715424

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().