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The Adjoint Method for the Inverse Problem of Option Pricing

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  • Shou-Lei Wang
  • Yu-Fei Yang
  • Yu-Hua Zeng

Abstract

The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the 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.

Suggested Citation

  • Shou-Lei Wang & Yu-Fei Yang & Yu-Hua Zeng, 2014. "The Adjoint Method for the Inverse Problem of Option Pricing," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, March.
    • Handle: RePEc:hin:jnlmpe:314104
    DOI: 10.1155/2014/314104
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    References listed on IDEAS

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