Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model
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 l...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-08-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/15/2480 |
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| Summary: | 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. |
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| ISSN: | 2227-7390 |