Bond Pricing with Jumps and Monte Carlo Simulation

  • Kisoeb Park
  • Moonseong Kim
  • Seki Kim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)


We derive a general form of the term structure of interest rates with jump. One-state models of Vasicek, CIR(Cox, Ingersol, and Ross), and the extended model of the Hull and White are introduced and the jump-diffusion models of the Ahn & Thompson and the Baz & Das as developed models are also investigated by using the Monte Carlo simulation which is one of the best methods in financial engineering to evaluate financial derivatives. We perform the Monte Carlo simulation with several scenarios even though it takes a long time to achieve highly precise estimates with the brute force method in terms of mean standard error which is one measure of the sharpness of the point estimates.


Interest Rate Monte Carlo Simulation Term Structure Spot Rate Bond Price 
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  1. 1.
    Ahn, C., Thompson, H.: Jump-Diffusion Processes and the Term Structure of Interest Rates. Journal of Finance 43, 155–174 (1998)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Baz, J., Das, S.R.: Analytical Approximations of the Term Structure for Jump-Diffusion Processes: A Numerical Analysis. Journal of Fixed Income 6(1), 78–86 (1996)CrossRefGoogle Scholar
  3. 3.
    Cox, J.C., Ingersoll, J., Ross, S.: A Theory of the Term Structure of Interest Rate. Econometrica 53, 385–407 (1985)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Health, D., Jarrow, R., Morton, A.: Bond Pricing and the Term Structure of Interest Rates. Econometrica 60(1), 77–105 (1992)CrossRefGoogle Scholar
  5. 5.
    Jamshidian, F.: An Exact Bond Option Formula. Journal of Finance 44 (1989)Google Scholar
  6. 6.
    Hull, J., White, A.: Pricing Interest Rate Derivative Securities. Review of Financial Studies 3, 573–592 (1990)CrossRefGoogle Scholar
  7. 7.
    Hull, J., White, A.: Options, Futures, and Derivatives, 4th edn (2000)Google Scholar
  8. 8.
    Brennan, M.J., Schwartz, E.S.: A Continuous Time Approach to the Pricing of Bonds. Journal of Banking and Finance 3, 133–155 (1979)CrossRefGoogle Scholar
  9. 9.
    Vasicek, O.A.: An Equilibrium Characterization of the Term Structure. Journal of Financial Economics 5, 177–188 (1977)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kisoeb Park
    • 1
  • Moonseong Kim
    • 2
  • Seki Kim
    • 1
  1. 1.Department of MathematicsSungkyunkwan UniversitySuwonKorea
  2. 2.School of Information and Communication EngineeringSungkyunkwan UniversitySuwonKorea

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