Vietnam Journal of Mathematics

, Volume 44, Issue 3, pp 513–530 | Cite as

Regularization for the Inverse Problem of Finding the Purely Time-Dependent Volatility

  • Dang Duc Trong
  • Dinh Ngoc Thanh
  • Nguyen Nhu LanEmail author


We consider the inverse problem of finding the volatility σL ρ (0, T) such that \(U_{BS}(X,K,r,t,{{\int }_{0}^{t}}\sigma ^{2}(\tau )d\tau )=u(t)\), 0≤tT, where U B S is the Black–Scholes formula and u(t) is the observable fair price of an European call option. The problem is ill-posed. Using the residual method, we shall regularize the problem. An explicit error estimate is given.


Calibration Volatility Ill-posed Regularization 

Mathematics Subject Classification (2010)

35R30 65J20 91B24 



The authors are grateful to three anonymous referees for their precious suggestions leading to the improvement version of our paper.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2015

Authors and Affiliations

  • Dang Duc Trong
    • 1
  • Dinh Ngoc Thanh
    • 1
  • Nguyen Nhu Lan
    • 2
    Email author
  1. 1.Department of Mathematics and Computer ScienceHo Chi Minh City University of Science, Vietnam National UniversityHo Chi Minh CityVietnam
  2. 2.Tay Do UniversityCan ThoVietnam

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