# Generalized Procedure for Building Short Rate Trees in Excel / VBA

In their 2014 paper John Hull and Alan White derive generalized method for the construction of short rate trees. This generalization is interesting as it allows for one tree (or lattice) construction algorithm for all one factor short rate models. The only difference between the various models is the function , which is explained briefly here and in detail in the paper. Continue reading

# Curiosities on the Monotone Preserving Cubic Spline

In this paper we describe some new features of the monotone-preserving cubic splines and the Hyman’s monotonicity constraint, that is implemented into various spline interpolation methods to ensure monotonicity. We find that, while the Hyman constraint is in general useful to enforce monotonicity, it can be safely omitted when the monotone-preserving cubic spline is considered. We also find that, when computing sensitivities, consistency requires making some specific assumptions about how to deal with non-differentiable locations, that become relevant for special values of the parameter space.

Keywords: Yield curve, fixed-income, interpolation, Hyman, monotone preserving cubic splines.