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2014 Calibration of the Volatility in Option Pricing Using the Total Variation Regularization
Yu-Hua Zeng, Shou-Lei Wang, Yu-Fei Yang
J. Appl. Math. 2014: 1-9 (2014). DOI: 10.1155/2014/510819

Abstract

In market transactions, volatility, which is a very important risk measurement in financial economics, has significantly intimate connection with the future risk of the underlying assets. Identifying the implied volatility is a typical PDE inverse problem. In this paper, based on the total variation regularization strategy, a bivariate total variation regularization model is proposed to estimate the implied volatility. We not only prove the existence of the solution, but also provide the necessary condition of the optimal control problem—Euler-Lagrange equation. The stability and convergence analyses for the proposed approach are also given. Finally, numerical experiments have been carried out to show the effectiveness of the method.

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Yu-Hua Zeng. Shou-Lei Wang. Yu-Fei Yang. "Calibration of the Volatility in Option Pricing Using the Total Variation Regularization." J. Appl. Math. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/510819

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07010661
MathSciNet: MR3191122
Digital Object Identifier: 10.1155/2014/510819

Rights: Copyright © 2014 Hindawi

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