On a consistent state-space bond markets model for pricing long-maturity bonds

In most financial markets, prices for long-maturity derivatives are not readily available due to illiquidity. This reality is particularly common in bond markets, as it is very challenging to model prices consistently—for medium-to-long-term bonds under a single specification of the underlying interest rate process. We develop a bond market state-space model that incorporates uncertainty in the underlying interest rate process parameters. Our state-space representation, coupled with the complementary Kalman filtering, provides a modeling configuration that permits for liquidity risk management and pricing that is designed in a consistent fashion for both medium- and long-term bonds. As an example, we constructed a state-space bond market modeling system formulated on the two-factor Vasicek interest rate model. Wherein, the interest rate model is subject to noise for medium-to-long-term bond maturities and follows an unobservable process. We demonstrate our Kalman filter algorithm using the observed United States (US) 10 year bond yield data.