원문정보
초록
영어
The reconstruction of a volatility based on a Black-Scholes option pricing model is ill-posed. In order to overcome the ill-posedness, a homotopy perturbation inversion method is designed to solve the inverse problem. The proposed method is a modified version of the Landweber method. The reconstruction of a volatility is a nonlinear problem which is needed to be linearized. Hence, numerical experiments consist of the reconstruction of a policy parameter based on a Todaro model which is a linear inverse problem and the reconstruction of a volatility based on a Black-Scholes option pricing model in order to test the performance of the proposed method. Numerical examples show that the proposed method is more accurate and faster than the Landweber method.
목차
1. Introduction
2. Mathematical Model
3. Solving Forward Problem using a Finite Difference Method
4. A Landweber Method for the Inverse Problem
5. A Homotopy Perturbation Inversion Method based on a Landweber Method
6. Extension to HPIM based on a Gauss-Newton Method
7. Numerical Experiments
7.1. Reconstruction of policy Parameter based on a Todaro Model (a linear case)
7.2. Reconstruction of Volatility Based on A Black-Scholes Option Pricing Model (a Nonlinear Case)
8. Conclusions
Acknowledgements
References