The Adjoint Method for the Inverse Problem of Option Pricing | Zendy

Shou-Lei Wang | Zendy; Yu-Fei Yang | Zendy; Zeng Yu-hua | Zendy

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The Adjoint Method for the Inverse Problem of Option Pricing

Author(s) -

Shou-Lei Wang,

Yu-Fei Yang,

Zeng Yu-hua

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/314104

Subject(s) - algorithm , minification , volatility (finance) , inverse problem , inverse , computer science , mathematics , mathematical optimization , mathematical analysis , econometrics , geometry

The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the TV-L1 model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS) to find the optimal and numerical examples shows the effectiveness of the presented method

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