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Interest rate theory

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Financial Mathematics

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Bibliography

  1. Artzner, P. & Delbaen, F. (1989) Term structure of interest rates. Advances in Applied Mathematics 10, 95–129.

    Article  MathSciNet  MATH  Google Scholar 

  2. Babbs, S. & Webber, N. (1993) A theory of the term structure with an official short rate. Working paper, University of Warwick.

    Google Scholar 

  3. Björk, T. (1995) On the term structure of discontinuous interest rates. Surveys in Industrial and Applied Mathematics 2 No.4, 626–657.

    Google Scholar 

  4. Björk, T. & Kabanov, Y. & Runggaldier, W. (1995) Bond market structure in the presence of marked point processes. Submitted to Mathematical Finance.

    Google Scholar 

  5. Björk, T. & Di Masi, G.& Kabanov, Y. & Runggaldier, W. (1995) Towards a general theory of bond markets. Finance and Stochastics. To appear.

    Google Scholar 

  6. Black, F. & Derman, E. & Toy, W. (1990) A one-factor model of interest rates and its application to treasury bond options. Finan. Analysts J. jan–feb, 33–39.

    Google Scholar 

  7. Brace, A. & Gatarek, D. & Musiela, M. (1995) The market model of interest rate dynamics. preprint. Dept. of Statistics. University of New South Wales, Australia.

    MATH  Google Scholar 

  8. Brace, A. & Musiela M. (1994) A multifactor Gauss Markov implementation of Health, Jarrow, and Morton. Mathematical Finance 4, 3, 259–283.

    Article  MATH  Google Scholar 

  9. Brémaud, P. (1981) Point Processes and Queues: Martingales Dynamics. Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  10. Brown, R.H. & Schaefer, S.M. (1994) Interest rate volatility and the shape of the term structure. Phil. Trans. R. Soc. Lond. A 347, 563–576.

    Article  MATH  Google Scholar 

  11. Cox, J. & Ingersoll, J. & Ross, S. (1985) A theory of the term structure of interest rates. Econometrica 53, 385–408.

    Article  MathSciNet  MATH  Google Scholar 

  12. Dana, R.-A. & Jeanblanc-Picqué M. (1994) Marchés Financiers en Temps Continu. Valorisation et Equilibre. Economica, Paris.

    Google Scholar 

  13. Delbaen, F. & Schachermayer, W. (1994) A general version of the fundamental theorem on asset pricing. Mathematische Annalen 300, 463–520.

    Article  MathSciNet  MATH  Google Scholar 

  14. Dellacherie, C & Meyer, P-A. (1972) Probabilités et Potentiel. Hermann, Paris.

    MATH  Google Scholar 

  15. Dothan, M. (1978) On the Term Structure of Interest Rates. Journal of Financial Economics 7, 229–264.

    Google Scholar 

  16. Duffie, D. (1992) Dynamic Asset Pricing Theory. Princeton Univ. Press.

    Google Scholar 

  17. Duffie, D. & Kan, R. (1993) A yield factor model of interest rates. Preprint, GSB Stanford University.

    Google Scholar 

  18. Duffie, D. & Singleton, K. (1995) Modeling of term structures of defaultable bonds. Working paper, Stanford University.

    Google Scholar 

  19. El Karoui, N. & Myneni, R. & Viswanathan, R. (1992) Arbitrage pricing and hedging of interest rate claims with state variable. I, II. Preprints, Laboratoire de Probabilités, Paris 6.

    Google Scholar 

  20. Elliott, R.J. (1982) Stochastic Calculus and Applications. Springer-Verlag, Berlin.

    MATH  Google Scholar 

  21. Geman, H. (1989) The importance of the forward neutral probability in a stochastic approach of interest rates. Working paper, ESSEC.

    Google Scholar 

  22. Geman, H. & El Karoui, N & Rochet, J-C. (1995) Changes of numéraire, changes of probability measure and option pricing. Journal of Applied Probability 32, 443–458.

    Article  MathSciNet  MATH  Google Scholar 

  23. Harrison, J.M. & Kreps, D. (1979) Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory 20, 381–408.

    Article  MathSciNet  MATH  Google Scholar 

  24. Harrison, J.M. & Pliska, S. (1981) Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes & Appl. 11, 215–260.

    Article  MathSciNet  MATH  Google Scholar 

  25. Heath, D. & Jarrow, R. & Morton, A. (1992) Bond pricing and the term structure of interest rates. Econometrica 60 No.1, 77–106.

    Article  MATH  Google Scholar 

  26. Ho, T. & Lee, S. (1986) Term structure movements and pricing interest rate contingent claims. Journal of Finance 41, 1011–1029.

    Article  Google Scholar 

  27. Hull, J. & White, A. (1990) Pricing interest-rate-derivative securities. The Review of Financial Studies 3, 573–592.

    Article  Google Scholar 

  28. Jacod, J. (1979) Calcul Stochastique et Problèmes de Martingales. LNM 714, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  29. Jacod, J. & Shiryaev A.N. (1987) Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  30. Jamshidian, F. (1989) An exact bond option formula. Journal of Finance 44, 205–209.

    Article  Google Scholar 

  31. Jarrow, R. & Lando D. & Turnbull S.M. (1995) A Markov model for the term stucture of credit risk spreads. Review of Financial Studies. To appear.

    Google Scholar 

  32. Jarrow, R. & Madan D. (1995) Option pricing using the term structure of interest rates to hedge systematic discontinuities in asset returns. Mathematical Finance 5 311–336.

    Article  MathSciNet  MATH  Google Scholar 

  33. Jarrow, R. & Madan D. (1995) Valuing and hedging contingent claims on semimartingales. Preprint.

    Google Scholar 

  34. Jarrow, R. & Turnbull. (1995) Pricing derivatives on financial securities subject to credit risk. Journal of Finance 50, 53–86.

    Article  Google Scholar 

  35. Lando, D. (1994) On Cox processes and credit risky bonds. Institute of Mathematical Statistics, University of Copanehagen.

    Google Scholar 

  36. Lindberg, H. & Orszag, M. & Perraudin, W. (1995) Yield curves with jump short rates. Preprint.

    Google Scholar 

  37. Longstaff, F. & Schwartz, E (1992) Valuing risky debt: A new approach. Workin paper, UCLA.

    Google Scholar 

  38. Merton, R. (1974) On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 2, 449–470.

    Google Scholar 

  39. Miltersen, K. & Sandmann, K. & Sondermann, D. (1995) Closed form solutions for term structure derivatives with log-normal interest rates. Dept. of management, Odense University, Denmark.

    Google Scholar 

  40. Musiela, M. (1993) Stochastic PDEs and term structure models. Preprint.

    Google Scholar 

  41. Musiela, M. & Rutkowski, M. Arbitrage Pricing of Derivative Securities. Theory and Applications. Preprint.

    Google Scholar 

  42. Platen, E. (1996) Explaining interest rate dynamics. Preprint. Centre for Financial mathematics, Australian National University, Canberra.

    Google Scholar 

  43. Platen, E. & Rebolledo, R. (1995) Principles for modelling financial markets. To appear in Advances in Applied Probability.

    Google Scholar 

  44. Protter, P. (1990) Stochastic Integration and Differential Equations. Springer-Verlag, Berlin.

    Book  MATH  Google Scholar 

  45. Rogers, L.C.G. (1995) The potential approach to the term structure of interest rates and foreign exchange rates. Preprint, University of Bath.

    Google Scholar 

  46. Rogers, L.C.G. (1995) Which model for term-structure of interest rates should one use?’ Mathematical Finance, IMA Volume 65, 93–116, Springer, New York.

    MATH  Google Scholar 

  47. Shimko, D. & Tejima, N. & van Deventer, D (1993) The pricing of risky debt when interest rates are stochastic. Journal of Fixed Income, September, 58–66.

    Article  Google Scholar 

  48. Shirakawa, H. (1991) Interest rate option pricing with Poisson-Gaussian forwrd rate curve processes. Mathematical Finance 1, 77–94.

    Article  MATH  Google Scholar 

  49. Vasiček, O. (1977) An equilibrium characterization of the term structure. Journal of Financial Economics 5, 177–188.

    Article  Google Scholar 

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Wolfgang J. Runggaldier

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Björk, T. (1997). Interest rate theory. In: Runggaldier, W.J. (eds) Financial Mathematics. Lecture Notes in Mathematics, vol 1656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091999

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  • DOI: https://doi.org/10.1007/BFb0091999

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