We investigate the term structure for the case when interest rates are allowed to be driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure, as well as completeness of the bond market. We also give sufficient conditions for the existence of an affine term structure. Developing the appropriate forward measures we give formulas for interest rate derivatives.
Introduction: One of the most challenging mathematical problems arising in the theory of financial markets concerns market completeness, i.e. the possibility of duplicating a contingent claim by a self- nancing portfolio. Informally,such a possibility arises whenever there are as many risky assets available for hedging as there are independent sources of randomness in the market.
Author: T. Björk, Y. Kabanov,W. Runggaldier
Source: Stockholm School of Economics
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