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Shape factors and cross-sectional risk

Author

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  • Andrea Roncoroni

    (ESSEC Business School)

  • Stefano Galluccio
  • Paolo Guiotto

    (Unipd - Università degli Studi di Padova = University of Padua)

Abstract

Galluccio and Roncoroni (2006) empirically demonstrate that cross-sectional data provide relevant information when assessing dynamic risk in fixed income markets. We put forward a theoretical framework supporting that finding based on the notion of "shape factors". We devise an econometric procedure to identify shape factors, propose a dynamic model for the yield curve, develop a corresponding arbitrage pricing theory, derive interest rate pricing formulae, and study the analytical properties exhibited by a finite factor restriction of rate dynamics that is cross-sectionally consistent with a family of exponentially weighed polynomials. We also conduct an empirical analysis of cross-sectional risk affecting US swap, Euro bond, and oil markets. Results support the conclusion whereby shape factors outperform the classical yield (resp. price) factors (i.e., level, slope, and convexity) in explaining the underlying fixed income (resp. commodity) market risk. The methodology can in principle be used for understanding the intertemporal dynamics of any cross-sectional data.

Suggested Citation

  • Andrea Roncoroni & Stefano Galluccio & Paolo Guiotto, 2010. "Shape factors and cross-sectional risk," Post-Print hal-00736733, HAL.
    • Handle: RePEc:hal:journl:hal-00736733
    DOI: 10.1016/j.jedc.2010.06.002
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    1. Engle, Robert F & Ng, Victor K, 1993. "Time-Varying Volatility and the Dynamic Behavior of the Term Structure," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(3), pages 336-349, August.
    2. Bertocchi, Marida & Giacometti, Rosella & Zenios, Stavros A., 2005. "Risk factor analysis and portfolio immunization in the corporate bond market," European Journal of Operational Research, Elsevier, vol. 161(2), pages 348-363, March.
    3. 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.
    4. Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1999. "Phenomenology of the interest rate curve," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 209-232.
    5. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    6. 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.
    7. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    8. Fong, H Gifford & Vasicek, Oldrich A, 1984. "A Risk Minimizing Strategy for Portfolio Immunization," Journal of Finance, American Finance Association, vol. 39(5), pages 1541-1546, December.
    9. 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..
    10. Pierre Collin‐Dufresne & Robert S. Goldstein & Christopher S. Jones, 2008. "Identification of Maximal Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 63(2), pages 743-795, April.
    11. Galluccio, Stefano & Roncoroni, Andrea, 2006. "A new measure of cross-sectional risk and its empirical implications for portfolio risk management," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2387-2408, August.
    12. Jouini,E. & Cvitanic,J. & Musiela,Marek (ed.), 2001. "Handbooks in Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521792370, September.
    13. Claudia La Chioma & Benedetto Piccoli, 2007. "Heath–Jarrow–Morton Interest Rate Dynamics And Approximately Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 427-447, July.
    14. Elton, Edwin J & Gruber, Martin J & Michaely, Roni, 1990. "The Structure of Spot Rates and Immunization," Journal of Finance, American Finance Association, vol. 45(2), pages 629-642, June.
    15. Heaney, W John & Cheng, Pao L, 1984. "Continuous Maturity Diversification of Default-Free Bond Portfolios and a Generalization of Efficient Diversification," Journal of Finance, American Finance Association, vol. 39(4), pages 1101-1117, September.
    16. Knez, Peter J & Litterman, Robert & Scheinkman, Jose Alexandre, 1994. "Explorations into Factors Explaining Money Market Returns," Journal of Finance, American Finance Association, vol. 49(5), pages 1861-1882, December.
    17. Robert R. Bliss, 1997. "Movements in the term structure of interest rates," Economic Review, Federal Reserve Bank of Atlanta, vol. 82(Q 4), pages 16-33.
    18. 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.
    19. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    20. Unknown, 2005. "Forward," 2005 Conference: Slovenia in the EU - Challenges for Agriculture, Food Science and Rural Affairs, November 10-11, 2005, Moravske Toplice, Slovenia 183804, Slovenian Association of Agricultural Economists (DAES).
    21. Erhan Bayraktar & Li Chen & H. Vincent Poor, 2006. "Projecting The Forward Rate Flow Onto A Finite Dimensional Manifold," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(05), pages 777-785.
    22. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283, July.
    23. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
    24. Prisman, Eliezer Z. & Shores, Marilyn R., 1988. "Duration measures for specific term structure estimations and applications to bond portfolio immunization," Journal of Banking & Finance, Elsevier, vol. 12(3), pages 493-504, September.
    25. Musiela, Marek, 1995. "General framework for pricing derivative securities," Stochastic Processes and their Applications, Elsevier, vol. 55(2), pages 227-251, February.
    26. Shin Ichi Aihara & Arunabha Bagchi, 2005. "Stochastic Hyperbolic Dynamics For Infinite‐Dimensional Forward Rates And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 27-47, January.
    27. 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.
    28. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    29. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
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    4. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2020. "Valuation of caps and swaptions under a stochastic string model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).

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