IDEAS home Printed from https://ideas.repec.org/b/spr/mathfi/v17y2023i2d10.1007_s11579-022-00331-7.html
   My bibliography  Save this book

A pricing formula for delayed claims: appreciating the past to value the future

Author

Listed:
  • Enrico Biffis

    (Imperial College London)

  • Beniamin Goldys

    (The University of Sydney)

  • Cecilia Prosdocimi

    (LUISS “Guido Carli”)

  • Margherita Zanella

    (Politecnico di Milano)

Abstract

We consider the valuation of contingent claims with delayed dynamics in a Samuelson complete market model. We find a pricing formula that can be decomposed into terms reflecting the current market values of the past and the future, showing how the valuation of prospective cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity. The formula we derive has successfully been used to explicitly solve the infinite dimensional stochastic control problems addressed in Biffis et al. (SIAM J Control Optim 58(4):1906–1938, 2020), Djeiche et al. (Stoch Process Appl 145:48–85, 2022) and Biagini et al. (SIAM J Financial Math 13(3):1004–1039, 2022).

Suggested Citation

  • Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2023. "A pricing formula for delayed claims: appreciating the past to value the future," Mathematics and Financial Economics, Springer, volume 17, number 2, February.
    • Handle: RePEc:spr:mathfi:v:17:y:2023:i:2:d:10.1007_s11579-022-00331-7
    DOI: 10.1007/s11579-022-00331-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11579-022-00331-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11579-022-00331-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Enrico Biffis & David Blake & Lorenzo Pitotti & Ariel Sun, 2016. "The Cost of Counterparty Risk and Collateralization in Longevity Swaps," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(2), pages 387-419, June.
    2. William T. Dickens & Lorenz Goette & Erica L. Groshen & Steinar Holden & Julian Messina & Mark E. Schweitzer & Jarkko Turunen & Melanie E. Ward, 2007. "How Wages Change: Micro Evidence from the International Wage Flexibility Project," Journal of Economic Perspectives, American Economic Association, vol. 21(2), pages 195-214, Spring.
    3. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. Faggian, Silvia & Gozzi, Fausto, 2010. "Optimal investment models with vintage capital: Dynamic programming approach," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 416-437, July.
    5. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
    6. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, vol. 18(1), pages 83-114, January.
    7. Hervé Le Bihan & Jérémi Montornès & Thomas Heckel, 2012. "Sticky Wages: Evidence from Quarterly Microeconomic Data," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(3), pages 1-32, July.
    8. Fatih Guvenen, 2007. "Learning Your Earning: Are Labor Income Shocks Really Very Persistent?," American Economic Review, American Economic Association, vol. 97(3), pages 687-712, June.
    9. Alessandro Barattieri & Susanto Basu & Peter Gottschalk, 2014. "Some Evidence on the Importance of Sticky Wages," American Economic Journal: Macroeconomics, American Economic Association, vol. 6(1), pages 70-101, January.
    10. Enrico Biffis & Fausto Gozzi & Cecilia Prosdocimi, 2020. "Optimal portfolio choice with path dependent labor income: the infinite horizon case," Papers 2002.00201, arXiv.org.
    11. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
    12. Costas Meghir & Luigi Pistaferri, 2004. "Income Variance Dynamics and Heterogeneity," Econometrica, Econometric Society, vol. 72(1), pages 1-32, January.
    13. Dybvig, Philip H. & Liu, Hong, 2010. "Lifetime consumption and investment: Retirement and constrained borrowing," Journal of Economic Theory, Elsevier, vol. 145(3), pages 885-907, May.
    14. 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.
    15. 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.
    16. Markus Reiß, 2002. "Minimax Rates for Nonparametric Drift Estimation in Affine Stochastic Delay Differential Equations," Statistical Inference for Stochastic Processes, Springer, vol. 5(2), pages 131-152, May.
    17. Abowd, John M & Card, David, 1989. "On the Covariance Structure of Earnings and Hours Changes," Econometrica, Econometric Society, vol. 57(2), pages 411-445, March.
    18. Djehiche, Boualem & Gozzi, Fausto & Zanco, Giovanni & Zanella, Margherita, 2022. "Optimal portfolio choice with path dependent benchmarked labor income: A mean field model," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 48-85.
    19. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2015. "A pricing formula for delayed claims: Appreciating the past to value the future," Papers 1505.04914, arXiv.org, revised Jul 2022.
    2. Enrico Biffis & Fausto Gozzi & Cecilia Prosdocimi, 2020. "Optimal portfolio choice with path dependent labor income: the infinite horizon case," Papers 2002.00201, arXiv.org.
    3. Fatih Guvenen & Burhanettin Kuruscu, 2010. "A Quantitative Analysis of the Evolution of the US Wage Distribution, 1970–2000," NBER Chapters, in: NBER Macroeconomics Annual 2009, Volume 24, pages 227-276, National Bureau of Economic Research, Inc.
    4. Tony Smith & M. Fatih Guvenen, 2007. "Inferring Labor Income Risk from Economic Choices: An Indirect Inference Approach," 2007 Meeting Papers 1024, Society for Economic Dynamics.
    5. repec:spo:wpecon:info:hdl:2441/6ggbvnr6munghes9od0s108ro is not listed on IDEAS
    6. Masakatsu Okubo, 2015. "Earnings Dynamics and Profile Heterogeneity: Estimates from Japanese Panel Data," The Japanese Economic Review, Japanese Economic Association, vol. 66(1), pages 112-146, March.
    7. Dmytro Hryshko, 2012. "Labor income profiles are not heterogeneous: Evidence from income growth rates," Quantitative Economics, Econometric Society, vol. 3(2), pages 177-209, July.
    8. Jeremy Lise & Costas Meghir & Jean-Marc Robin, 2016. "Matching, Sorting and Wages," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 19, pages 63-87, January.
    9. Jeremy Lise & Costas Meghir & Jean-Marc Robin, 2013. "Mismatch, Sorting and Wage Dynamics," Cowles Foundation Discussion Papers 1886, Cowles Foundation for Research in Economics, Yale University.
    10. Gregory Veramendi, 2012. "Labor Market Dynamics: A Model of Search and Human Capital Accumulation," 2012 Meeting Papers 1059, Society for Economic Dynamics.
    11. Robin Jessen & Johannes König, 2023. "Hours risk and wage risk: repercussions over the life cycle," Scandinavian Journal of Economics, Wiley Blackwell, vol. 125(4), pages 956-996, October.
    12. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2009. "Quantitative Macroeconomics with Heterogeneous Households," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 319-354, May.
    13. Fatih Guvenen, 2009. "An Empirical Investigation of Labor Income Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(1), pages 58-79, January.
    14. Joseph G. Altonji & Anthony A. Smith Jr. & Ivan Vidangos, 2013. "Modeling Earnings Dynamics," Econometrica, Econometric Society, vol. 81(4), pages 1395-1454, July.
    15. Lance Lochner & Youngki Shin, 2014. "Understanding Earnings Dynamics: Identifying and Estimating the Changing Roles of Unobserved Ability, Permanent and Transitory Shocks," NBER Working Papers 20068, National Bureau of Economic Research, Inc.
    16. Estelle Dauchy & Francisco Navarro-Sanchez & Nathan Seegert, 2021. "Taxation and Inequality: Active and Passive Channels," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 42, pages 156-177, October.
    17. Richard Blundell & Hamish Low & Ian Preston, 2013. "Decomposing changes in income risk using consumption data," Quantitative Economics, Econometric Society, vol. 4(1), pages 1-37, March.
    18. Benjamin Friedrich & Costas Meghir & Lisa Laun & Luigi Pistaferri, 2018. "Earnings Dynamics and Firm-Level Shocks," 2018 Meeting Papers 536, Society for Economic Dynamics.
    19. Hyungsik Roger Moon & Frank Schorfheide & Boyuan Zhang, 2023. "Bayesian Estimation of Panel Models under Potentially Sparse Heterogeneity," PIER Working Paper Archive 23-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    20. repec:spo:wpmain:info:hdl:2441/6ggbvnr6munghes9od0s108ro is not listed on IDEAS
    21. repec:hal:journl:hal-01070442 is not listed on IDEAS
    22. Koray Aktas, 2021. "Characterizing Life-Cycle Dynamics of Annual Days of Work, Wages, and Cross-Covariances," Working Papers 465, University of Milano-Bicocca, Department of Economics.
    23. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2014. "Consumption and Labor Supply with Partial Insurance: An Analytical Framework," American Economic Review, American Economic Association, vol. 104(7), pages 2075-2126, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathfi:v:17:y:2023:i:2:d:10.1007_s11579-022-00331-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.