tailieunhanh - Bond Market Structure in the Presence of Marked Point Processes

investors in the stock market also hold bond funds to help smooth out the inevitable fluctuations in the value of their overall investment portfolios. Although bond funds can fluctuate in value just as stock funds do, bond funds do not always move in the same direction or to the same degree as stock funds. | Bond Market Structure in the Presence of Marked Point Processes Tomas Bjork Department of Finance Stockholm School of Economics Box 6501 S-113 83 Stockholm SWEDEN Yuri Kabanov Central Economics and Mathematics Institute Russian Academy of Sciences and Laboratoire de Mathematiques Universite de Franche-Comté 16 Route de Gray F-25030 Besangon Cedex FRANCE Wolfgang Runggaldier Dipartimento di Matematica Pura et Applicata Universita di Padova Via Belzoni 7 35131 Padova ITALY February 28 1996 Submitted to Mathematical Finance The financial support and hospitality of the University of Padua the Isaac Newton Institute Cambridge University and the Stockholm School of Economics are gratefully acknowledged. 1 Abstract We investigate the term structure of zero coupon bonds when interest rates are 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. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jump spectrum we give a fairly general completeness result and for a Wiener-Poisson model we prove the existence of a time- independent set of basic bonds. We also give sufficient conditions for the existence of an affine term structure. Key words bond market term structure of interest rates jumpdiffusion model measure-valued portfolio arbitrage market completeness martingale operator hedging operator affine term structure. 1 Introduction One of the most challenging mathematical problems arising in the theory of financial markets concerns market completeness . the possibility of duplicating a contingent claim by a self-financing 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. In bond markets as well as in stock markets it seems reasonable to take .