Startseite Reconstruction of local volatility surface from American options
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Reconstruction of local volatility surface from American options

  • Wenxiu Gong und Zuoliang Xu EMAIL logo
Veröffentlicht/Copyright: 31. Mai 2022

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.

MSC 2010: 65M32; 91G60

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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Received: 2019-11-16
Revised: 2021-12-18
Accepted: 2022-03-07
Published Online: 2022-05-31
Published in Print: 2023-02-01

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