| Report ID: | 06-11-81654-28 |
| Initial Submission Date: | 2006-11-08 |
| Title: | Piecewise Polynomial Replication Strategies and Moment Matrices in Convex Optimization based Option |
| Summary: | This paper develops a framework for optimization based bounds on option prices by using piecewise polynomial sub or super replicating strategies of existing options and assets whose value at discrete time points can be represented as piecewise polynomial functions. The optimization problems are presented as polynomial programs which can be modified to a convex optimization problem using the sum-of-squares methodology. The dual approach is then developed by relaxing a martingale pricing problem to an optimization problem involving moment matrices of measures consistent with martingale pricing measures. Both formulations use semidefinite programming to bound option prices while also being able to consistently incorporate existing option price data. Computation of the bounds is demonstrated using data consistent with the standard Black-Scholes option pricing model and Mertons jump diffusion model. |
| Authors: | Primbs, James |
| Contact email: | japrimbs@stanford.edu |
| | Number of views : 784 Number of downloads : 400 |
