TAILIEUCHUNG - TOWARDS A GENERAL THEORY OF BOND MARKETS

As the study of natural catastrophe models plays an important role in the preven- tion and mitigation of disasters, the main motivation of this paper is the analysis of pricing CAT bonds. In particular, we examine the calibration of a parametric CAT bond for earthquakes that was sponsored by the Mexican government and issued by the special purpose CAT-MEX Ltd in May 2006. The calibration of the CAT bond is based on the estimation of the intensity rate that describes the earthquakes process from the two sides of the contract: from the reinsurance market that consists of the sponsor company (the Mexican government) and the issuer of reinsurance. | Towards a general theory of bond markets Tomas Bjork Department of Finance Stockholm School of Economics Box 6501 S-113 83 Stockholm SWEDEN Giovanni Di Masi Dipartimento di Matematica Pura et Applicata Universitá di Padova Via Belzoni 7 35131 Padova ITALY Yuri Kabanov Central Economics and Mathematics Institute of the Russian Academy of Sciences and Laboratoire de Mathématiques Université de Franche-Comté 16 Route de Gray F-25030 Besancon Cedex FRANCE Wolfgang Runggaldier Dipartimento di Matematica Pura et Applicata Universitá di Padova Via Belzoni 7 35131 Padova ITALY To appear in Finance and Stochastics T11C financial support and hospitality of the University of Padua the Isaac Newton Institute Cambridge University and the Stockholm School of Economics arc gratefully acknowledged. 1 To memory of our friend and colleague Oliviero Lessi. Abstract The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding to a trading strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show that a market is approximately complete iff an equivalent martingale measure is unique. Key words bond market term structure of interest rates stochastic integral Banach space-valued integrators measure-valued portfolio jump-diffusion model martingale measure arbitrage market completeness. 1 Introduction In the last few years a remarkable progress has been made in the understanding of bond .

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