Abstract: The invention provides systems and methods for providing replicable financial instrument orders, and establishing a fill price that is better than the theoretical upper limit of the industries' best order execution. The system has the capability of transforming a client's index order into a replicable product, such as index futures and/or baskets of the underlying stocks. The system selects whichever method and combination of securities that will achieve the best expected execution for the particular market. The system achieves the best price and execution efficiency by utilizing dynamic market information across all possible liquidity formats, liquidity pools, and high performance trading systems, delivering a product that has multiple forms at the best possible price. The result is a better final execution price that outperforms current industry practices for best order execution.

Abstract: There are provided new structural default models for modeling the likely default of publicly traded companies. In a first embodiment, the invention is straight-forward to implement and allows the capture of some important ingredients of the actual default, including positive short-term CDSs. In a second embodiment the model is somewhat more versatile and complex. Provided is a very efficient method for dealing with the timing of a default boundary, that is, jumps in the company's value, etc. Further provided is a process using Fast Fourier Transform matrix processing for processing the structural default models in a computationally efficient manner.