A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing
AbstractOur goal is to identify the volatility function in Dupire's equation from given option prices. Following an optimal control approach in a Lagrangian framework, we propose a globalized sequential quadratic programming (SQP) algorithm with a modified Hessian - to ensure that every SQP step is a descent direction - and implement a line search strategy. In each level of the SQP method a linear-quadratic optimal control problem with box constraints is solved by a primal-dual active set strategy. This guarantees L1 constraints for the volatility, in particular assuring its positivity. The proposed algorithm is founded on a thorough first- and second-order optimality analysis. We prove the existence of local optimal solutions and of a Lagrange multiplier associated with the inequality constraints. Furthermore, we prove a sufficient second-order optimality condition and present some numerical results underlining the good properties of the numerical scheme.
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Bibliographic InfoPaper provided by Center of Finance and Econometrics, University of Konstanz in its series CoFE Discussion Paper with number 06-02.
Length: 27 pages
Date of creation: 29 Mar 2006
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-08-26 (All new papers)
- NEP-CFN-2006-08-26 (Corporate Finance)
- NEP-ETS-2006-08-26 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
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