A Sequential Quadratic Programming Method For Volatility Estimation In Option Pricing
A Sequential Quadratic Programming Method For Volatility Estimation In Option Pricing
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2006
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CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie; 2006/02
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Our 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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330 Wirtschaft
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option pricing
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DÜRING, Bertram, Ansgar JÜNGEL, Stefan VOLKWEIN, 2006. A Sequential Quadratic Programming Method For Volatility Estimation In Option PricingBibTex
@techreport{During2006Seque-521, year={2006}, series={CoFE-Diskussionspapiere / Zentrum für Finanzen und Ökonometrie}, title={A Sequential Quadratic Programming Method For Volatility Estimation In Option Pricing}, number={2006/02}, author={Düring, Bertram and Jüngel, Ansgar and Volkwein, Stefan} }
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