Arbitrage-Free Yield Curve

We address the issue of market incompleteness in the time dimension. Specifically, we focus on interest rate markets and the yield curve extraction. The lack of information about interest rates manifest itself in a non-invertible linear system. The usual approach to circumvent this problem is by applying various curve fitting methods - both parametric and non-parametric. We argue in favor of a novel method relying on information theory, which reformulates the ill-posed linear algebra problem into a well-posed optimization problem, where the linear pricing equations are used as constraints. Local cross entropy is used to determine the optimal solution among the admissible solutions, while all the input prices reflected in constraints are perfectly matched. Large-scale optimization package called AMPL is used extensively throughout this work to obtain the optimal solution as well as to demonstrate the implementation details.