Search results for " SQP method"

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A Sequential Quadratic Programming Method for Volatility Estimation in Option Pricing

2006

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 L^1 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 existe…

Hessian matrixMathematical optimizationLine searchComputer scienceMathematicsofComputing_NUMERICALANALYSISOptimal controlsymbols.namesakeValuation of optionsLagrange multipliersymbolsDescent directionVolatility (finance)Dupire equation parameter identification optimal control optimality conditions SQP method primal-dual active set strategySequential quadratic programming
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