IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v22y2018i4d10.1007_s00780-018-0370-x.html
   My bibliography  Save this article

Sensitivity analysis of long-term cash flows

Author

Listed:
  • Hyungbin Park

    (Seoul National University)

Abstract

This paper conducts a sensitivity analysis of long-term cash flows. The price of the cash flow at time zero is given by the pricing operator of a Markov diffusion acting on the cash flow function. We study the extent to which the price of the cash flow is affected by small perturbations of the underlying Markov diffusion. The main tool is the Hansen–Scheinkman decomposition, which is a method to express the cash flow in terms of eigenvalues and eigenfunctions of the pricing operator. By incorporating techniques developed by Fournié et al. (Finance Stoch. 3:391–412, 1999), the sensitivities of long-term cash flows can be represented via simple expressions in terms of eigenvalues and eigenfunctions.

Suggested Citation

  • Hyungbin Park, 2018. "Sensitivity analysis of long-term cash flows," Finance and Stochastics, Springer, vol. 22(4), pages 773-825, October.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:4:d:10.1007_s00780-018-0370-x
    DOI: 10.1007/s00780-018-0370-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-018-0370-x
    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/s00780-018-0370-x?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. Jaroslav Borovička & Lars P. Hansen & Jose A. Scheinkman, 2014. "Shock Elasticities and Impulse Responses," NBER Working Papers 20104, National Bureau of Economic Research, Inc.
    2. Youssef El-Khatib & Nicolas Privault, 2004. "Computations of Greeks in a market with jumps via the Malliavin calculus," Finance and Stochastics, Springer, vol. 8(2), pages 161-179, May.
    3. Lars Peter Hansen & José A. Scheinkman, 2009. "Long-Term Risk: An Operator Approach," Econometrica, Econometric Society, vol. 77(1), pages 177-234, January.
    4. Davis, Mark H.A. & Johansson, Martin P., 2006. "Malliavin Monte Carlo Greeks for jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 101-129, January.
    5. D. Baños & T. Meyer-Brandis & F. Proske & S. Duedahl, 2017. "Computing deltas without derivatives," Finance and Stochastics, Springer, vol. 21(2), pages 509-549, April.
    6. Tim Leung & Ronnie Sircar, 2015. "Implied Volatility of Leveraged ETF Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 162-188, April.
    7. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    8. Bernard Wong & C. C. Heyde, 2006. "On changes of measure in stochastic volatility models," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-13, December.
    9. Eric Benhamou, 2003. "Optimal Malliavin Weighting Function for the Computation of the Greeks," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 37-53, January.
    10. Likuan Qin & Vadim Linetsky, 2016. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing," Operations Research, INFORMS, vol. 64(1), pages 99-117, February.
    11. Lars Peter Hansen, 2012. "Dynamic Valuation Decomposition Within Stochastic Economies," Econometrica, Econometric Society, vol. 80(3), pages 911-967, May.
    12. Lars Hansen & José Scheinkman, 2012. "Pricing growth-rate risk," Finance and Stochastics, Springer, vol. 16(1), pages 1-15, January.
    13. Chen, Nan & Glasserman, Paul, 2007. "Malliavin Greeks without Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1689-1723, November.
    14. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hyungbin Park, 2021. "Influence of risk tolerance on long-term investments: A Malliavin calculus approach," Papers 2104.00911, arXiv.org.
    2. Hyungbin Park, 2021. "Modified Mean-Variance Risk Measures for Long-Term Portfolios," Mathematics, MDPI, vol. 9(2), pages 1-23, January.
    3. Hyungbin Park & Heejun Yeo, 2022. "Dynamic and static fund separations and their stability for long-term optimal investments," Papers 2212.00391, arXiv.org, revised Mar 2023.
    4. Hyungbin Park, 2019. "Convergence rates of large-time sensitivities with the Hansen--Scheinkman decomposition," Papers 1912.03404, arXiv.org, revised Jan 2021.

    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. Hyungbin Park, 2021. "Influence of risk tolerance on long-term investments: A Malliavin calculus approach," Papers 2104.00911, arXiv.org.
    2. Hyungbin Park, 2015. "Sensitivity Analysis of Long-Term Cash Flows," Papers 1511.03744, arXiv.org, revised Sep 2018.
    3. Tim Leung & Hyungbin Park, 2017. "LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-33, September.
    4. Hyungbin Park & Heejun Yeo, 2022. "Dynamic and static fund separations and their stability for long-term optimal investments," Papers 2212.00391, arXiv.org, revised Mar 2023.
    5. Hyungbin Park, 2019. "Convergence rates of large-time sensitivities with the Hansen--Scheinkman decomposition," Papers 1912.03404, arXiv.org, revised Jan 2021.
    6. Hyungbin Park, 2014. "Pricing and Hedging Long-Term Options," Papers 1410.8160, arXiv.org, revised Mar 2016.
    7. Borovicka, J. & Hansen, L.P., 2016. "Term Structure of Uncertainty in the Macroeconomy," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 1641-1696, Elsevier.
    8. Jaroslav Borovička & Lars P. Hansen & Jose A. Scheinkman, 2014. "Shock Elasticities and Impulse Responses," NBER Working Papers 20104, National Bureau of Economic Research, Inc.
    9. Likuan Qin & Vadim Linetsky, 2018. "Long-term factorization in Heath–Jarrow–Morton models," Finance and Stochastics, Springer, vol. 22(3), pages 621-641, July.
    10. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    11. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    12. Anselm Hudde & Ludger Rüschendorf, 2023. "European and Asian Greeks for Exponential Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    13. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2019. "Gauge transformations in the dual space, and pricing and estimation in the long run in affine jump-diffusion models," Papers 1912.06948, arXiv.org, revised Dec 2019.
    14. Muroi, Yoshifumi & Suda, Shintaro, 2017. "Computation of Greeks in jump-diffusion models using discrete Malliavin calculus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 140(C), pages 69-93.
    15. Hansen, Lars Peter & Sargent, Thomas J., 2021. "Macroeconomic uncertainty prices when beliefs are tenuous," Journal of Econometrics, Elsevier, vol. 223(1), pages 222-250.
    16. Hansen, Lars Peter, 2013. "Risk Pricing over Alternative Investment Horizons," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1571-1611, Elsevier.
    17. Likuan Qin & Vadim Linetsky, 2014. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery and Long-Term Pricing," Papers 1411.3075, arXiv.org, revised Sep 2015.
    18. Likuan Qin & Vadim Linetsky, 2016. "The Long Bond, Long Forward Measure and Long-Term Factorization in Heath-Jarrow-Morton Models," Papers 1610.00818, arXiv.org, revised Jul 2017.
    19. El-Khatib, Youssef & Abdulnasser, Hatemi-J, 2011. "On the calculation of price sensitivities with jump-diffusion structure," MPRA Paper 30596, University Library of Munich, Germany.
    20. Dillschneider, Yannick & Maurer, Raimond, 2019. "Functional Ross recovery: Theoretical results and empirical tests," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).

    More about this item

    Keywords

    Long-term cash flows; Hansen–Scheinkman decomposition; Sensitivity analysis;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

    Statistics

    Access and download statistics

    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:finsto:v:22:y:2018:i:4:d:10.1007_s00780-018-0370-x. 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.