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Quadratic Gaussian Joint Pricing Model for Stocks and Bonds: Theory and Empirical Analysis

Author

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  • Kentaro Kikuchi

    (Faculty of Economics, Shiga University)

Abstract

This study proposes a joint pricing model for stocks and bonds in a no-arbitrage framework. A stock price representation is obtained in a manner consistent with the quadratic Gaussian term structure model, in which the short rate is the quadratic form of the state variables. In this study, specifying the dividend as a function using the quadratic form of the state variables leads to a stock price representation that is exponential-quadratic in the state variables. We prove that the coefficients determining the stock price have to satisfy some matrix equations, including an algebraic Riccati equation. Moreover, we specify the sufficient condition in which the matrix equations do have a unique solution. In our empirical analysis using Japanese data, we obtain estimates with a good fit to the actual data. Furthermore, we estimate the risk premiums for stocks and bonds and analyze how the BOJ's unconventional monetary policy has affected these risk premiums.

Suggested Citation

  • Kentaro Kikuchi, 2015. "Quadratic Gaussian Joint Pricing Model for Stocks and Bonds: Theory and Empirical Analysis," Discussion Papers CRR Discussion Paper Series B: Financial 14, Shiga University, Faculty of Economics,Center for Risk Research.
    • Handle: RePEc:shg:dpapeb:14
    as

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    File URL: https://www.econ.shiga-u.ac.jp/risk/DPB14kikuchi20150107.pdfFile-Format:Application/pdf
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    References listed on IDEAS

    as
    1. Werner, Thomas & Lemke, Wolfgang, 2009. "The term structure of equity premia in an affine arbitrage-free model of bond and stock market dynamics," Working Paper Series 1045, European Central Bank.
    2. Leippold, Markus & Wu, Liuren, 2002. "Asset Pricing under the Quadratic Class," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(2), pages 271-295, June.
    3. d'Addona, Stefano & Kind, Axel H., 2006. "International stock-bond correlations in a simple affine asset pricing model," Journal of Banking & Finance, Elsevier, vol. 30(10), pages 2747-2765, October.
    4. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
    5. L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176, April.
    6. Harry Mamaysky, 2002. "On the Joint Pricing of Stocks and Bonds: Theory and Evidence," Yale School of Management Working Papers ysm256, Yale School of Management.
    7. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    risk premium; quadratic Gaussian term structure model; unscented Kalman filter; algebraic Riccati equation; controllability; portfolio rebalance;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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