An Essay on stochastic discount factor decomposition

Abstract

In this work, we use the framework developed by Christensen (2017) and Hansen and Scheinkman (2009) to study the long-term interest rates in the US and Brazil. In our first set of results, we assess Christensen (2017) estimator using Monte Carlo simulations in order to evaluate the estimator performance in the rare disasters and habit formation asset pricing models. Generally, the estimation quality is not uniform and, in some cases, requires a large sample size to attain reasonable results. Next, we apply the nonparametric estimation to US and Brazilian data and estimate how the yield of a long-term zero-coupon bond responds to the initial state of the economy. Using a flexible specification for the state process leads to an interesting non-linear response of the yield to changes in the initial state. We find that the Brazilian long-term interest rate is about 5.3% per year.