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A term structure model for dividends and interest rates

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  • Damir Filipović
  • Sander Willems

Abstract

Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump‐diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method for option pricing. In a calibration exercise we show that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 Index dividend futures and dividend options, and Euro Stoxx 50 Index options.

Suggested Citation

  • Damir Filipović & Sander Willems, 2020. "A term structure model for dividends and interest rates," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1461-1496, October.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:4:p:1461-1496
    DOI: 10.1111/mafi.12279
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    as
    1. Holly, Alberto & Monfort, Alain & Rockinger, Michael, 2011. "Fourth order pseudo maximum likelihood methods," Journal of Econometrics, Elsevier, vol. 162(2), pages 278-293, June.
    2. M. H. Vellekoop & J. W. Nieuwenhuis, 2006. "Efficient Pricing of Derivatives on Assets with Discrete Dividends," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 265-284.
    3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    4. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 143-159, March.
    5. R. S. Tunaru, 2018. "Dividend derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 63-81, January.
    6. Damir Filipovi'c & Sander Willems, 2016. "Exact Smooth Term-Structure Estimation," Papers 1606.03899, arXiv.org, revised Aug 2018.
    7. Damir Filipovic & Damien Ackerer & Sergio Pulido, 2018. "The Jacobi Stochastic Volatility Model," Post-Print hal-01338330, HAL.
    8. Geiß, Christel & Manthey, Ralf, 1994. "Comparison theorems for stochastic differential equations in finite and infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 23-35, September.
    9. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. Rockinger, Michael & Jondeau, Eric, 2002. "Entropy densities with an application to autoregressive conditional skewness and kurtosis," Journal of Econometrics, Elsevier, vol. 106(1), pages 119-142, January.
    12. Lettau, Martin & Wachter, Jessica A., 2011. "The term structures of equity and interest rates," Journal of Financial Economics, Elsevier, vol. 101(1), pages 90-113, July.
    13. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    14. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    15. Sander Willems, 2019. "Asian option pricing with orthogonal polynomials," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 605-618, April.
    16. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    17. Weber, Michael, 2018. "Cash flow duration and the term structure of equity returns," Journal of Financial Economics, Elsevier, vol. 128(3), pages 486-503.
    18. 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.
    19. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    20. Geert Bekaert & Steven R. Grenadier, 1999. "Stock and Bond Pricing in an Affine Economy," NBER Working Papers 7346, National Bureau of Economic Research, Inc.
    21. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    22. Kragt, Jac & de Jong, Frank & Driessen, Joost, 2020. "The Dividend Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(3), pages 829-867, May.
    23. Damien Ackerer & Damir Filipović, 2020. "Linear credit risk models," Finance and Stochastics, Springer, vol. 24(1), pages 169-214, January.
    24. 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.
    25. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
    26. Geske, Robert, 1978. "The Pricing of Options with Stochastic Dividend Yield," Journal of Finance, American Finance Association, vol. 33(2), pages 617-625, May.
    27. repec:hal:journl:peer-00815562 is not listed on IDEAS
    28. Damien Ackerer & Damir Filipović & Sergio Pulido, 2018. "The Jacobi stochastic volatility model," Finance and Stochastics, Springer, vol. 22(3), pages 667-700, July.
    29. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    30. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
    31. Barone-Adesi, Giovanni & Rasmussen, Henrik & Ravanelli, Claudia, 2005. "An option pricing formula for the GARCH diffusion model," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 287-310, April.
    32. Damir Filipović & Martin Larsson & Anders B. Trolle, 2017. "Linear-Rational Term Structure Models," Journal of Finance, American Finance Association, vol. 72(2), pages 655-704, April.
    33. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    34. G. Fusai & A. Tagliani, 2002. "An Accurate Valuation Of Asian Options Using Moments," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 147-169.
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    5. Ed-Dafali, Slimane & Patel, Ritesh & Iqbal, Najaf, 2023. "A bibliometric review of dividend policy literature," Research in International Business and Finance, Elsevier, vol. 65(C).

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