Bond Market Structure in the Presence of Marked Point Processes

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 that 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.

[1]  Robert Jarrow,et al.  Hedging contingent claims on semimartingales , 1999, Finance Stochastics.

[2]  N. Webber,et al.  A Theory of the Term Structure with an Official Short Rate , 1998 .

[3]  Tomas Björk,et al.  Towards a general theory of bond markets , 1997, Finance Stochastics.

[4]  W. Perraudin,et al.  Yield Curves with Jump Short Rates , 1996 .

[5]  Y. Kabanov,et al.  Bond Markets Where Prices are Driven by a General Marked Point Process , 1995 .

[6]  Robert A. Jarrow,et al.  OPTION PRICING USING THE TERM STRUCTURE OF INTEREST RATES TO HEDGE SYSTEMATIC DISCONTINUITIES IN ASSET RETURNS1 , 1995 .

[7]  Jean-Charles Rochet,et al.  Changes of numéraire, changes of probability measure and option pricing , 1995, Journal of Applied Probability.

[8]  F. Delbaen,et al.  A general version of the fundamental theorem of asset pricing , 1994 .

[9]  Marek Musiela,et al.  A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton , 1994 .

[10]  S. Schaefer,et al.  Interest rate volatility and the shape of the term structure , 1994, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[11]  Rose-Anne Dana,et al.  Marchés financiers en temps continu : valorisation et équilibre , 1994 .

[12]  D. Duffie.  Dynamic Asset Pricing Theory , 1992 .

[13]  Hiroshi Shirakawa,et al.  Interest Rate Option Pricing with Poisson-Gaussian Forward Rate Curve Processes , 1991 .

[14]  D. Heath,et al.  Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation , 1990, Journal of Financial and Quantitative Analysis.

[15]  Alan G. White,et al.  Pricing Interest-Rate-Derivative Securities , 1990 .

[16]  P. Protter.  Stochastic integration and differential equations , 1990 .

[17]  B. Malkiel.  Term Structure of Interest Rates , 1989 .

[18]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[19]  S. Ross,et al.  A theory of the term structure of interest rates'', Econometrica 53, 385-407 , 1985 .

[20]  D. Sworder.  Stochastic calculus and applications , 1984, IEEE Transactions on Automatic Control.

[21]  P. Brémaud.  Point processes and queues, martingale dynamics , 1983 .

[22]  Robert J. Elliott,et al.  Stochastic calculus and applications , 1984, IEEE Transactions on Automatic Control.

[23]  J. Harrison,et al.  Martingales and stochastic integrals in the theory of continuous trading , 1981 .

[24]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[25]  A. Irturk,et al.  Term Structure of Interest Rates , 2006 .

[26]  Oldrich A. Vasicek.  An equilibrium characterization of the term structure , 1977 .

[27]  P. Meyer,et al.  Probabilités et potentiel , 1966 .