Abstract
In this paper, we discuss the reconstruction of a local volatility surface from American option prices. First of all, the American option prices are calculated by an accurate and fast finite difference scheme. Then the local volatility is obtained by minimizing the distance between theoretical prices and market option prices, which yields an optimization problem. The Bicubic spline regularization technique is used to overcome the ill-posedness of the reconstruction problem. We solve the nonlinear optimization problem by using a gradient-based optimization algorithm. Finally, we test our model with numerical examples and real market American put option data. The results show the good performance of our method.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 12071479
Award Identifier / Grant number: 11571365
Funding statement: The work is supported by National Natural Science Foundation of China (12071479, 11571365).
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Multi-coil MRI by analytic continuation
- The factorization method for a penetrable cavity scattering with interior near-field measurements
- Method for solving inverse spectral problems on quantum star graphs
- On mixed and transverse ray transforms on orientable surfaces
- Robust signal recovery via ℓ1–2/ℓ𝑝 minimization with partially known support
- Interior reconstruction in tomography via prior support constrained compressed sensing
- Reconstruction of local volatility surface from American options
- Stability for the electromagnetic inverse source problem in inhomogeneous media
- Scalar and vector tomography for the weighted transport equation with application to helioseismology
- Secant-type iteration for nonlinear ill-posed equations in Banach space
Artikel in diesem Heft
- Frontmatter
- Multi-coil MRI by analytic continuation
- The factorization method for a penetrable cavity scattering with interior near-field measurements
- Method for solving inverse spectral problems on quantum star graphs
- On mixed and transverse ray transforms on orientable surfaces
- Robust signal recovery via ℓ1–2/ℓ𝑝 minimization with partially known support
- Interior reconstruction in tomography via prior support constrained compressed sensing
- Reconstruction of local volatility surface from American options
- Stability for the electromagnetic inverse source problem in inhomogeneous media
- Scalar and vector tomography for the weighted transport equation with application to helioseismology
- Secant-type iteration for nonlinear ill-posed equations in Banach space