Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model
Abstract
1. Introduction
2. Direct Problem
2.1. Analytical Solution for Constant Volatility
2.2. Numerical Method for Variable Volatility
2.3. Stability and Convergence Analyses
3. Inverse Problem
Linearization at Constant Volatility
4. Numerical Examples
4.1. Numerical Results for Direct Problem
4.2. Numerical Simulation for Inverse Problem
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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No. of Time Steps | No. of Spatial Steps | Err | |
---|---|---|---|
1001 | 17 | 0.1029 | |
1001 | 33 | 0.0302 | 1.7686 |
1001 | 65 | 0.0098 | 1.6237 |
1001 | 129 | 0.0036 | 1.4448 |
1001 | 257 | 0.0012 | 1.5850 |
1001 | 513 | 1.7407 |
No. of Time Steps | No. of Spatial Steps | Err | |
---|---|---|---|
201 | 1024 | 0.0880 | |
401 | 1024 | 0.0421 | 1.0599 |
801 | 1024 | 0.0191 | 1.1423 |
1601 | 1024 | 0.0077 | 1.3106 |
3201 | 1024 | 0.0019 | 2.0189 |
1.4 | 1.5 | 1.6 | 1.7 | 1.8 | 1.9 | |
---|---|---|---|---|---|---|
errors | 0.7329 | 0.2192 | 0.2647 | 0.2323 | 0.1559 | 0.1168 |
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Jiang, X.; Shi, C.; Wei, Y. Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model. Mathematics 2025, 13, 2480. https://doi.org/10.3390/math13152480
Jiang X, Shi C, Wei Y. Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model. Mathematics. 2025; 13(15):2480. https://doi.org/10.3390/math13152480
Chicago/Turabian StyleJiang, Xiaoying, Chunmei Shi, and Yujie Wei. 2025. "Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model" Mathematics 13, no. 15: 2480. https://doi.org/10.3390/math13152480
APA StyleJiang, X., Shi, C., & Wei, Y. (2025). Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model. Mathematics, 13(15), 2480. https://doi.org/10.3390/math13152480