Toward a unified model of sovereign quanto CDS spreads and government bond yields

Abstract

A unified model that consistently evaluates sovereign quanto credit default swap (CDS) and government bonds is developed. By product, a new procedure is proposed to calibrate stochastic processes of the risk-free interest rate and the sovereign default intensity to sovereign quanto CDS spreads and government bond yields. Fractional step methods are applied to solve partial differential equations for CDS spreads and bond yields, which cannot be solved using a standard finite difference method due to a cross derivative term. An empirical study is conducted on United States, German and Portuguese quanto CDS spreads during the European sovereign debt crisis. The stochastic processes of the riskfree interest rates in USD and Euros and the default intensities of United States, German and Portuguese are simultaneously estimated and reveals that sovereign quanto CDS spread differentials are partially explained by introducing a correlation between the risk-free interest rate and the sovereign default intensity. Numerical analysis shows that the larger correlation between them leads to the smaller CDS spread.