Identification of the local speed function in a Lévy model for option pricing. (English) Zbl 1149.91034
This paper proposes a non-parametric stable calibration method based on Tikhonov regularization for the local speed function in a local Lévy model. The jump term in this model introduces an operator into the classical Black-Scholes equation such that the associated model calibration to observed option prices can be treated as a parameter identification problem for a partial integro-differential equation. This problem is ill-posed and thus requires regularization. The paper proves that nonlinear Tikhonov regularization is a stable and convergent method. Convergence rates are established and numerical illustrations given.
Reviewer: Pedro A. Morettin (São Paulo)
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 65J20 | Numerical solutions of ill-posed problems in abstract spaces; regularization |
| 65R30 | Numerical methods for ill-posed problems for integral equations |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
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