Reconstruction of local volatility surface from American options-Reference-Cited by-同舟云学术

Reconstruction of local volatility surface from American options

Published:2022-05-31 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Gong Wenxiu¹,Xu Zuoliang²

Affiliation:

1. College of Mathematics and Systems Science , Shandong University of Science and Technology , 266590 Qingdao , P. R. China

2. School of Mathematics , Renmin University of China , 100872 Beijing , P. R. China

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2019-0085/pdf

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