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Market Price of Risk Specifications for Affine Models: Theory and Evidence

  • Patrick Cheridito
  • Damir Filipovic
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    We extend the standard specification of the market price of risk for affine yield models of the term structure of interest rates, and estimate several models using the extended specification. For most models, the extended specification fits US data better than standard specifications, often with extremely high statistical significance. Our specification yields models that are affine under both objective and risk-neutral probability measures, but is never used in financial applications, probably because of the difficulty of applying traditional methods for proving the absence of arbitrage. Using an alternate method, we show that the extended specification does not permit arbitrage opportunities, provided that under both measures the state variables cannot achieve their boundary values. Likelihood ratio tests show our extension is statistically significant for four of the models considered at the conventional 95% confidence level, and at far higher levels for three of the models. The results are particularly strong for affine diffusions with multiple square-root type variables. Although we focus on affine yield models, our extended market price of risk specification also applies to any model in which Feller's square-root process or a multivariate extension is used to model asset prices.

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    Paper provided by Econometric Society in its series Econometric Society 2004 North American Winter Meetings with number 536.

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    Date of creation: 11 Aug 2004
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    Handle: RePEc:ecm:nawm04:536
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    1. Ait-Sahalia, Yacine & Kimmel, Robert L., 2008. "Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions," Working Paper Series 2008-19, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    3. 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.
    4. Pearson, Neil D & Sun, Tong-Sheng, 1994. " Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
    5. 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.
    6. 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.
    7. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    8. Yacine Ait-Sahalia, 2002. "Closed-Form Likelihood Expansions for Multivariate Diffusions," NBER Working Papers 8956, National Bureau of Economic Research, Inc.
    9. Brandt, Michael W. & Santa-Clara, Pedro, 2002. "Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets," Journal of Financial Economics, Elsevier, vol. 63(2), pages 161-210, February.
    10. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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