A penalty approach to a discretized double obstacle problem with derivative constraints

This work presents a penalty approach to a nonlinear optimization problem with linear box constraints arising from the discretization of an infinite-dimensional differential obstacle problem with bound constraints on derivatives. In this approach, we first propose a penalty equation approximating the mixed nonlinear complementarity problem representing the Karush-Kuhn-Tucker conditions of the optimization problem. We then show that the solution to the penalty equation converges to that of the complementarity problem with an exponential convergence rate depending on the parameters used in the equation. Numerical experiments, carried out on a non-trivial test problem to verify the theoretical finding, show that the computed rates of convergence match the theoretical ones well

Term structure information and bond strategies

We examine term structure theories by using a novel approach. We form bond investment strategies based on different theories of the term structure in order to determine which strategy performs best. When using a manipulation-proof performance measure, we find that consistent with prior literature, an active strategy that is based on time varying term premiums can indeed form the basis of a successful bond strategy that outperforms an unbiased expectation inspired passive bond buy and hold strategy. This is true, however, for an earlier time period when the literature first made this claim. In a later time period, we find that the passive buy and hold strategy is significantly superior to all active strategies. This result is confirmed by statistical tests and it suggests that once it became known that an active strategy based on time varying term premiums could outperform a passive buy and hold strategy, the markets adjusted and arbitraged away this opportunity. Overall, it appears that the unbiased expectation hypothesis is the most likely explanation of the behaviour of the term structure during more recent times. This is because economically and statistically significant superior performance cannot be achieved if one uses information from the forward curve or the term structure as a guide to adjusting bond portfolios in response to changes in the term premium.This work was supported by Junta de Comunidades de Castilla-La Mancha [grant number PEII11-0031-6939]; Ministerio de Ciencia e Innovación [grant number ECO2011-28134] and partially supported by Fondo Europeo de Desarrollo Regional (FEDER) funds.