In:
Journal of Applied Mathematics, Hindawi Limited, Vol. 2014 ( 2014), p. 1-9
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.
Type of Medium:
Online Resource
ISSN:
1110-757X
,
1687-0042
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2014
detail.hit.zdb_id:
2578385-3
SSG:
17,1
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