Self-financing trading strategies for sliding, rolling-horizon, and consol bonds (Q2757309)

The sliding bond process with time to maturity \(T\) at the time \(t\) describes the price of the (\(T+t)\)-matured discount bond at \(t\). This process does not represent the wealth of a self-financing trading strategy. In the present work, the author examines the price dynamics of the sliding bond by constructing appropriate self-financed trading strategies whose wealth is intend to mimic the slide bond process. The first part of the paper deals with discrete time setting, while in the second part the results are generalized to continuous time, which requires techniques for integration of measure-valued processes to capture infinite number of assets (bonds with different maturities) in the portfolio. For discrete time, the author derives stochastic difference equation for slide bond process which shows that under local martingale measure the discounted slide bond follows a supermartingale if the forward rate is nonnegative. Further considerations deal with the rolling-horizon bond, the consol-bond, and the rolling-consol bond, and the price dynamics for these assets is determined. For continuous time, the author obtains a stochastic differential equation describing the evolution of slide bond without making specific reference on particular dynamics of the instantaneous forward rates. Again, the dynamics of the rolling-horizon bond, of the console bond and of the rolling-console bond are calculated and their specializations to the case of the Heath-Jarrow-Morton model are discussed.