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A Novel Approach to Asset Pricing with Choice of Probability Measures

Author

Listed:
  • Taiga Saito

    (Faculty of Economics, The University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, The University of Tokyo)

Abstract

This paper presents a foundation and concrete examples of yield curve models incorporating fundamental uncertainties, that is, uncertainties about Brownian motions representing fundamental market risks. Firstly, to model aggressive (positive)/conservative (cautious) attitudes towards such fundamental uncertainties, we consider a sup-inf/inf-sup problem on the utility of a representative agent with respect to uncertainties over Brownian motions, i.e. fundamental market risks. Secondly, we show that the problem is solved via a backward-stochastic differential equations (BSDEs) approach. Then, under a probability measure determined by solving the sup-inf/inf-sup problem, we propose interest rate models with those uncertainties and explicitly obtain their term structures of interest rates. Particularly, we present two approaches to solving the relevant coupled forward-backward stochastic differential equations (FBSDEs) to obtain expressions of the equilibrium interest rate and the term structure of interest rates. In detail, the first approach is by comparison theorems, and the second approach is to predetermine the signs of the volatilities of the BSDE in the coupled system and confirm them by explicitly solving the separated BSDE. Finally, we present concrete examples with numerical experiments.

Suggested Citation

  • Taiga Saito & Akihiko Takahashi, 2019. "A Novel Approach to Asset Pricing with Choice of Probability Measures," CIRJE F-Series CIRJE-F-1131, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2019cf1131
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    References listed on IDEAS

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    1. Hisashi Nakamura & Wataru Nozawa & Akihiko Takahashi, 2009. "Macroeconomic Implications of Term Structures of Interest Rates Under Stochastic Differential Utility with Non-Unitary EIS," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(3), pages 231-263, September.
    2. Urszula Szczerbowicz, 2015. "The ECB Unconventional Monetary Policies: Have They Lowered Market Borrowing Costs for Banks and Governments?," International Journal of Central Banking, International Journal of Central Banking, vol. 11(4), pages 91-127, December.
    3. Kiyohiko G. Nishimura & Seisho Sato & Akihiko Takahashi, 2019. "Term Structure Models During the Global Financial Crisis: A Parsimonious Text Mining Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 26(3), pages 297-337, September.
    4. Joyce, Michael, 2012. "Quantitative easing and other unconventional monetary policies: Bank of England conference summary," Bank of England Quarterly Bulletin, Bank of England, vol. 52(1), pages 48-56.
    5. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    6. Michael Joyce & David Miles & Andrew Scott & Dimitri Vayanos, 2012. "Quantitative Easing and Unconventional Monetary Policy – an Introduction," Economic Journal, Royal Economic Society, vol. 122(564), pages 271-288, November.
    7. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    8. Taiga Saito & Akihiko Takahashi, 2017. "Derivatives Pricing with Market Impact and Limit Order Book," CARF F-Series CARF-F-385, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Hisashi Nakamura & Keita Nakayama & Akihiko Takahashi, 2008. "Term Structure of Interest Rates under Recursive Preferences in Continuous Time," CIRJE F-Series CIRJE-F-540, CIRJE, Faculty of Economics, University of Tokyo.
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    Cited by:

    1. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2019. "Online Appendix for Interest Rate Model with Investor Attitude and Text Mining," CIRJE F-Series CIRJE-F-1136, CIRJE, Faculty of Economics, University of Tokyo.
    2. Souta Nakatani & Kiyohiko G. Nishimura & Taiga Saito & Akihiko Takahashi, 2019. "Online Appendix for Interest Rate Model with Investor Attitude and Text Mining," CARF F-Series CARF-F-470, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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