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Complex Times: Asset Pricing and Conditional Moments under Non-affine Diffusions

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  • Kimmel, Robert L.

    (Ohio State U)

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    Abstract

    Many applications in financial economics require calculation of conditional moments or contingent claims prices, but such expressions are known in closed-form for only a few specific models. We develop a method for approximation of such quantities, using power series, for a large class of non-affine diffusions and interest rate specifications. We also introduce a family of non-affine transformations of time that often dramatically improve the convergence properties of the power series approximations. In many cases, the approximations are uniformly accurate for arbitrarily long time horizons, and are therefore suitable for applications such as bond pricing, in which the time-to-maturity may be many years. The ability to approximate solutions accurately and in closed-form simplifies the estimation of non-affine continuous-time term structure models, since the bond pricing problem must be solved for many different parameter vectors during a typical estimation procedure. We show through a bond pricing example that the approximations are easy to derive and highly accurate over a wide range of interest rate levels for arbitrarily long maturities.

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    File URL: http://www.cob.ohio-state.edu/fin/dice/papers/2007/2007-6.pdf
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    Bibliographic Info

    Paper provided by Ohio State University, Charles A. Dice Center for Research in Financial Economics in its series Working Paper Series with number 2007-6.

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    Date of creation: Apr 2007
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    Handle: RePEc:ecl:ohidic:2007-6

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    1. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
    2. Jarrow, Robert & Li, Haitao & Liu, Sheen & Wu, Chunchi, 2010. "Reduced-form valuation of callable corporate bonds: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 95(2), pages 227-248, February.
    3. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
    4. Sergei Levendorskii, 2004. "Consistency conditions for affine term structure models," Papers cond-mat/0404107, arXiv.org.
    5. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 379-404.
    6. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-62.
    7. Georg Mosburger & Paul Schneider, 2005. "Modelling International Bond Markets with Affine Term Structure Models," Finance 0509003, EconWPA.
    8. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
    9. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January.
    10. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
    11. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    12. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    13. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    14. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    16. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
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