## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014 (2014), Article ID 510819, 9 pages.

### Calibration of the Volatility in Option Pricing Using the Total Variation Regularization

Yu-Hua Zeng, Shou-Lei Wang, and Yu-Fei Yang

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#### 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.

#### Article information

**Source**

J. Appl. Math., Volume 2014 (2014), Article ID 510819, 9 pages.

**Dates**

First available in Project Euclid: 2 March 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1425305633

**Digital Object Identifier**

doi:10.1155/2014/510819

**Mathematical Reviews number (MathSciNet)**

MR3191122

**Zentralblatt MATH identifier**

07010661

#### Citation

Zeng, Yu-Hua; Wang, Shou-Lei; Yang, Yu-Fei. Calibration of the Volatility in Option Pricing Using the Total Variation Regularization. J. Appl. Math. 2014 (2014), Article ID 510819, 9 pages. doi:10.1155/2014/510819. https://projecteuclid.org/euclid.jam/1425305633

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