Discrete Affine Term Structure Models Applied to German and Greek Government Bonds

This paper has two parts. The first part will explore and document discrete time affine term structure models in a similar setup as seen in the celebrated papers from Backus, Foresi, Telmer (1998 and 1996) and Backus, Telmer and Wu (1999). However, the paper will concentrate on the multifactor case under Vasicek (1977) and Cox-Ingersoll-Ross (1985) and unify some of the notation taking into account some of the developments seen on Duffie and Kan (1996), Piazzesi (2010) and Cochrane (2005) as well as Singleton (2006). The second half concentrates in calibrating the models and presents discussion of results, which are encouraging. When the economy is booming risk free assets' yields are expected to flatten and when the economy is under recession risk free assets' yields such as German sovereign bonds are expected to steepen. A different picture is observed for Greek Government bonds, which we show are governed mainly by deficit-to-GDP ratio, unemployment rate and debt-to-GDP ratio. Greece, in times of financial distress exhibits a downward sloping yield curve and yields are highly correlated to increases in unemployment and increases to its sovereign debt-to-GDP ratio. For the case of Greece it is also observed that a deterioration of the budget deficit-to-GDP ratio results in a fall in Greek government yields, however, a deterioration of the debt-to-GDP ratio together with an increase in unemployment more than offset this effect, resulting in an overall rise in the yields and hence, in a further deterioration of the financial position.