A Pure Test for the Elasticity of Yield Spreads

Canadian callable bond indices is largely due to the call premium, while this relationship is
negligible for noncallable bonds. This result is robust for a variety of empirical models, and
still holds for an inflation-adjusted test.

The remainder of this paper is organized as follows. The next section introduces
previous studies and their empirical models and describes the unique characteristics of the
Canadian bond market. Section 3 outlines the data and regression methodology and presents
the empirical results. In section 4, an alternative test using default rates is undertaken. Finally,
the summary and conclusion are offered in section 5.

2. Previous Studies

The two factor valuation model of Longstaff and Schwartz (1995) is an extension of the
closed-form solution of Merton (1974), where default is a function of the value of the firm at
maturity, to a simple continuous-time valuation framework that allows for both default and
interest rate risk. This structural model captures the stochastic nature of interest rates, where
for simplicity the dynamics of the interest rate are explained using a simple term structure
model based on Vasicek (1977). Other perspectives include the reduced-form models of
Jarrow, Lando and Turnbull (1997) and Duffie and Singleton (1999) where the payoff upon
default is specified exogenously, The asset level which triggers default can also be imposed
endogenously by having the shareholders optimally liquidate the firm as in Leland (1994),
Leland and Toft (1996) and Anderson and Sundaresan (1996). As noted by Giesecke (2006)
these models do not consider the way information is revealed over time, and implicitly
assume that investors can observe the inputs to the model definition of default. However,
investors do not have complete information about the inputs to the model definition of
default; in particular the asset value of a firm is hard to directly observe. Consequently in her
model, termed a first passage default model, investors learn over time the location of the
barrier, since it must lie below the observable historical low of assets to date if the firm has
not already defaulted.

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