| Article ID: | iaor200912341 |
| Country: | United States |
| Volume: | 139 |
| Issue: | 3 |
| Start Page Number: | 515 |
| End Page Number: | 540 |
| Publication Date: | Dec 2008 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Dring B, Jngel A, Volkwein S |
| Keywords: | programming: quadratic |
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, a globalized sequential quadratic programming (SQP) algorithm combined with a primal–dual active set strategy is proposed. Existence of local optimal solutions and of Lagrange multipliers is shown. Furthermore, a sufficient second–order optimality condition is proved. Finally, some numerical results are presented underlining the good properties of the numerical scheme.