Pricing callable bonds by means of green's function

Mathematical Finance

Volumn 6, Issue 1, 1996, Pages 53-88

  Büttler, Hans Jürg ^a   Waldvogel, Jörg ^b  

^a SWISS NATIONAL BANK   (Switzerland)

^b ETH ZURICH   (Switzerland)

Author keywords

Callable bond; Green's function; Numerical quadrature; Orthogonal polynomials; Series solution of the partial differential equation to value a discount bond

Indexed keywords

EID: 0040203968     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9965.1996.tb00112.x     Document Type: Article

References (40)

1. ABADIR, KARIM (1993): "On the Asymptotic Power of Unit Root Tests," Econometric Theory, 9, 189-221.
2. ABRAMOWITZ, MILTON, and IRENE A. STEGUN (eds.) (1965): Handbook of Mathematical Functions, 9th ed. New York: Dover.
3. ARTZNER, PHILIPPE, and FREDDY DELBAEN (1989): "Term Structure of Interest Rate: The Martingale Approach," Adv. Appl. Math., 10, 95-129.
4. BEAGLEHOLE, DAVID R., and MARK S. TENNEY (1991): "General Solutions of Some Interest Rate-Contingent Claim Pricing Equations," J. Fixed Income, 2, 69-83.
5. BRENNAN, MICHAEL J., and EDUARDO S. SCHWARTZ (1977): "Savings Bonds, Retractable Bonds and Callable Bonds," J. Financial Econom., 5, 67-88.
6. BRENNAN, MICHAEL J., and EDUARDO S. SCHWARTZ (1979): "A Continuous Time Approach to the Pricing of Bonds," J. Banking Finance, 3, 133-155.
7. BÜTTLER, HANS-JURG (1995): "Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy," Econom. J., 105, 374-384.
8. CHAN, K. C., G. A. KAROLYI, F. A. LONGSTAFF, and A. B. SANDERS (1992): "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," J. Finance, 47, 1209-1227.
9. CHEN, REN-RAW, and LOUIS SCOTT (1992): "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," Rev. Financial Stud., 5, 613-636.
10. -x f (x) dx by Gauss-Laguerre quadrature," Math. Comput., 17, 245-265.
11. COX, JOHN C., JONATHAN E. INGERSOLL, JR., and STEPHEN A. ROSS (1985a): "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, 53, 363-384.
12. COX, JOHN C., JONATHAN E. INGERSOLL, JR., and STEPHEN A. ROSS ( 1985b): "A Theory of the Term Structure of Interest Rates," Econometrica, 53, 385-407.
13. DEBOOR, CARL (1978): A Practical Guide to Splines. New York: Springer-Verlag.
14. DUFFIE, DARRELL (1992): Dynamic Asset Pricing Theory. Princeton, NJ: Princeton University Press.
15. ERDÉLYI, ARTHUR, WILHELM MAGNUS, FRITZ OBERHETTINGER, and FRANCESCO G. TRICOMI (1953): Higher Transcendental Functions, vol. 1-3. New York: McGraw-Hill.
16. ERDÉLYI, ARTHUR, WILHELM MAGNUS, FRITZ OBERHETTINGER, and FRANCESCO G. TRICOMI (1954): Tables of Integral Transforms, vol. 1, 2. New York: McGraw-Hill.
17. FELLER, WILLIAM (1951): "Two Singular Diffusion Problems," Ann. Math., 54, 173-182.
18. FELLER, WILLIAM (1952): "The Parabolic Differential Equations and the Associated Semi-groups of Transformations," Ann. Math., 55, 468-519.
19. FRITSCH, F. N., and R. E. CARLSON (1980): "Monotone Piecewise Cubic Interpolation," SIAM J. Numer. Anal., 17, 238-246.
20. GIBSON-ASNER, RAJNA (1990): "Valuing Swiss Default-free Callable Bonds," J. Banking Finance, 14, 649-672.
21. GOLUB, GENE H., and JOHN H. WELSH (1969): "Calculation of Gauss Quadrature Rules," Math. Comput., 23, 221-230.
22. HENRICI, PETER (1974): Applied and Computational Complex Analysis, vol. 1. New York: Wiley.
23. HENRICI, PETER (1982): Essentials of Numerical Analysis with Pocket Calculator Demonstrations. New York: Wiley.
24. IRI, M., S. MORIGUTI, and Y. TAKASAWA (1970): "On a Certain Quadrature Formula," RIMS Kokyuroku Kyoto Univ., 91, 82-118.
25. JAMSHIDIAN, FARSHID (1989): "An Exact Bond Option Formula," J. Finance, 44, 205-209.
26. JAMSHIDIAN, FARSHID (1991 a): "Bond and Option Evaluation in the Gaussian Interest Rate Model," Res. Finance, 9, 131-170.
27. JAMSHIDIAN, FARSHID (1991b): "Forward Induction and Construction of Yield Curve Diffusion Models," Working Paper, Financial Strategies Group, Merrill Lynch.
28. JENSEN, KATHLEEN, and NIKLAUS WIRTH (1982): Pascal: User Manual and Report, 2nd ed. New York: Springer-Verlag.
29. JOHNSON, NORMAN L., and SAMUEL KOTZ (eds.) (1970): Continuous Univariate Distributions, vols. 1, 2. New York: Wiley.
30. LEITHNER, STEPHAN (1992): Valuation and Risk Management of Interest Rate Derivative Securities. Bern: Verlag Paul Haupt.
31. PITMAN, JIM, and MARC YOR (1982): "A Decomposition of Bessel Bridges," Z. Wahrsch. Geb., 59, 425-457.
32. PRESS, WILLIAM H., BRIAN P. FLANNERY, SAUL A. TEUKOLSKY, and WILLIAM T. VETTERLING (1989): Numerical Recipes in Pascal: The Art of Scientific Computing, Cambridge University Press.
33. SCHWARTZ, C. (1969): "Numerical Integration of Analytic Functions," J. Comput. Phys., 4, 19-29.
34. SCHWARZ, HANS RUDOLF (1986): Numerische Mathematik, 2nd ed. Stuttgart: B. G. Teubner.
35. SMITH, G. D. (1985): Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed. Oxford, Clarendon Press.
36. SZEGÖ, GABOR (1939): Orthogonal Polynomals, Providence, RI: American Mathematical Society, Colloquium Publications, vol. 23.
37. TAKAHASHI, H., and M. MORI (1974): "Double Exponential Formulas for Numerical Integration," Publ. RIMS Kokyuroku Kyoto Univ., 9, 721-741.
38. TIKU, M. (1981): "Noncentral Chi-Square Distribution," in Encyclopedia of Statistical Sciences, eds. SAMUEL KOTZ and NORMAN L. JOHNSON. New York: Wiley.
39. VASICEK, OLDRICH (1977): "An Equilibrium Characterization of the Term Structure," Journal of Financial Economics, 5, 177-188.
40. WALDVOGEL, JÖRG (1988): "Numerical Quadrature in Several Dimensions," Int. Ser. Numer. Math., 85, 295-309.