Arbitrage-free multifactor term structure models: a theory based on stochastic control (Q2851559)

The problem of pricing bonds and bond derivatives in a multifactor model for the interest rate is analysed. The authors present an alternative way of studying that problem. The method is based on the solution of an optimal stochastic control problem. By providing a link between stochastic control theory and the classical martingale approach, a new representation of prices and forward price bonds under multifactor structure is also provided. The main novelty of the methodology resides in the change of drift. The authors' method, in contrast to the classical martingale approach, changes the drift without changing the measure. The method also provides a new insight showing the equivalence of calculating prices using a traditional change of measure and using the solution of an optimal control problem. That allows for the construction of computational pricing algorithms using control theory methods. It also allows for the presentation of explicit expressions to calculate the prices of options on bonds in the linear-quadratic case. The authors present the mathematical setting of the problem as well as several propositions with their proofs. Results are given in a general form, and, in Section 4 of the work, the particular form of an exponential quadratic term structure is analysed in more detail. At the end, the authors present some concluding remarks as well as some possible extensions of their work.