Consumption Skewness, Time Deformation and the Term Structure

We model the effect of consumption skewness on the unconditional shape of the term structure using a time deformation model with a persistent component in the stochastic clock. In the spirit of the ‘rare disaster’ representation of climate change, we specify a ‘pure’ jump model for consumption. Negative skewness in consumption reduces the level of the long-term interest rate. The slope of the term structure is determined by the common component in the stochastic clock, which has a natural economic representation as an increase in the clock of disasters. The model was specified to the case of a Gamma-distributed clock, corresponding to a Variance Gamma (VG) model. The VG model also allows us to split the increase in negative skewness in the difference between the expected rate of negative jumps (disasters) and that of positive jumps (bonanzas).