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A Stochastic String with a Compound Poisson Process

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  • Sheng Fan

Abstract

We investigate a compound Poisson infinite factor diffusion model which describes the relationship between the infinite‐dimension random risk resource and the corresponding stochastic process. We derive the no‐arbitrage condition on the drift of instantaneous forward rates in the compound model and study the impact of random jump on the price of the zero‐coupon bond.

Suggested Citation

  • Sheng Fan, 2013. "A Stochastic String with a Compound Poisson Process," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:857678
    DOI: 10.1155/2013/857678
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    References listed on IDEAS

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    1. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(4), pages 419-440, December.
    2. Ernst Eberlein & Jean Jacod & Sebastian Raible, 2005. "Lévy term structure models: No-arbitrage and completeness," Finance and Stochastics, Springer, vol. 9(1), pages 67-88, January.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Santa-Clara, Pedro & Sornette, Didier, 2001. "The Dynamics of the Forward Interest Rate Curve with Stochastic String Shocks," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 149-185.
    5. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258, July.
    6. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    7. Goldstein, Robert S, 2000. "The Term Structure of Interest Rates as a Random Field," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 365-384.
    8. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    9. D. P. Kennedy, 1997. "Characterizing Gaussian Models of the Term Structure of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 107-118, April.
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    Cited by:

    1. Sheng Fan, 2014. "The Analysis of Corporate Bond Valuation under an Infinite Dimensional Compound Poisson Framework," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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