Empirically Effective Bond Pricing Model and Analysis on Term Structures of Implied Interest Rates in Financial Crisis

Abstract

In his book (1993) Kariya proposed a government bond (GB) pricing model that simultaneously values individual fixed-coupon (non-defaultable) bonds of different coupon rates and maturities via a discount function approach, and Kariya and Tsuda (Financ Eng Japanese Mark 1:1–20, 1994) verified its empirical effectiveness of the model as a pricing model for Japanese Government bonds (JGBs) though the empirical setting was limited to a simple case. In this paper we first clarify the theoretical relation between our stochastic discount function approach and the spot rate or forward rate approach in mathematical finance. Then we make a comprehensive empirical study on the capacity of the model in view of its pricing capability for individual GBs with different attributes and in view of its capacity of describing the movements of term structures of interest rates that JGBs imply as yield curves. Based on various tests of validity in a GLS (Generalized Least Squares) framework we propose a specific formulation with a polynomial of order 6 for the mean discount function that depends on maturity and coupon as attributes and a specific covariance structure. It is shown that even in the middle of the Financial Crisis, the cross-sectional model we propose is shown to be very effective for simultaneously pricing all the existing JGBs and deriving and describing zero yields.