IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v51y2014icp1-11.html
   My bibliography  Save this article

Learning, pricing, timing and hedging of the option to invest for perpetual cash flows with idiosyncratic risk

Author

Listed:
  • Song, Dandan
  • Wang, Huamao
  • Yang, Zhaojun

Abstract

The paper considers the option of an investor to invest in a project that generates perpetual cash flows, of which the drift parameter is unobservable. The investor invests in a liquid financial market to partially hedge cash flow risk and estimation risk. We derive two 3-dimensional non-linear free-boundary PDEs satisfied by the utility-based prices of the option and cash flows. We provide an approach to measure the information value. A numerical procedure is developed. We show that investors have not only idiosyncratic-risk-induced but also estimation-risk-induced precautionary saving demands. A growth of estimation risk, risk aversion or project risk delays investment, but it is accelerated if the project is more closely correlated with the market. Partial information results in a considerable loss, which reaches the peak value at the exercising time and increases with project risk and estimation risk. The more risk-averse the investor or the weaker the correlation, the larger the loss.

Suggested Citation

  • Song, Dandan & Wang, Huamao & Yang, Zhaojun, 2014. "Learning, pricing, timing and hedging of the option to invest for perpetual cash flows with idiosyncratic risk," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 1-11.
    • Handle: RePEc:eee:mateco:v:51:y:2014:i:c:p:1-11
    DOI: 10.1016/j.jmateco.2014.02.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406814000378
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2014.02.009?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. Fernando Alvarez & Francesco Lippi, 2014. "Price Setting With Menu Cost for Multiproduct Firms," Econometrica, Econometric Society, vol. 82(1), pages 89-135, January.
    2. Christian-Oliver Ewald & Zhaojun Yang, 2008. "Utility based pricing and exercising of real options under geometric mean reversion and risk aversion toward idiosyncratic risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 97-123, August.
    3. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    4. Gennotte, Gerard, 1986. "Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-746, July.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Miao, Jianjun & Wang, Neng, 2007. "Investment, consumption, and hedging under incomplete markets," Journal of Financial Economics, Elsevier, vol. 86(3), pages 608-642, December.
    7. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    8. Zhaojun Yang & Chaoqun Ma, 2001. "Optimal Trading Strategy With Partial Information And The Value Of Information: The Simplified And Generalized Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(05), pages 759-772.
    9. Robert McDonald & Daniel Siegel, 1986. "The Value of Waiting to Invest," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 101(4), pages 707-727.
    10. Wang, Neng, 2009. "Optimal consumption and asset allocation with unknown income growth," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 524-534, May.
    11. Jinqiang Yang & Zhaojun Yang, 2012. "Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 195-217, February.
    12. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    13. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
    14. Henderson, Vicky & Hobson, David G., 2002. "Real options with constant relative risk aversion," Journal of Economic Dynamics and Control, Elsevier, vol. 27(2), pages 329-355, December.
    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. Yang, Zhaojun & Zhang, Chunhong, 2015. "Two new equity default swaps with idiosyncratic risk," International Review of Economics & Finance, Elsevier, vol. 37(C), pages 254-273.
    2. Goodarzi, Milad & Meinerding, Christoph, 2023. "Asset allocation with recursive parameter updating and macroeconomic regime identifiers," Discussion Papers 06/2023, Deutsche Bundesbank.
    3. Xiaolin Wang & Zhaojun Yang & Pingping Zeng, 2023. "Pricing contingent convertibles with idiosyncratic risk," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 660-693, September.
    4. Zhaojun Yang, 2020. "Investment and asset securitization with an option‐for‐guarantee swap," European Financial Management, European Financial Management Association, vol. 26(4), pages 1006-1030, September.

    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. Jinqiang Yang & Zhaojun Yang, 2012. "Consumption Utility-Based Pricing and Timing of the Option to Invest with Partial Information," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 195-217, February.
    2. Dandan Song & Zhaojun Yang, 2014. "Utility-Based Pricing, Timing and Hedging of an American Call Option Under an Incomplete Market with Partial Information," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 1-26, June.
    3. Carol Alexander & Xi Chen, 2021. "Model risk in real option valuation," Annals of Operations Research, Springer, vol. 299(1), pages 1025-1056, April.
    4. Ewald, Christian Oliver & Taub, Bart, 2022. "Real options, risk aversion and markets: A corporate finance perspective," Journal of Corporate Finance, Elsevier, vol. 72(C).
    5. Xiaolin Wang & Zhaojun Yang & Pingping Zeng, 2023. "Pricing contingent convertibles with idiosyncratic risk," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 660-693, September.
    6. Ewald, Christian-Oliver & Wang, Wen-Kai, 2010. "Irreversible investment with Cox-Ingersoll-Ross type mean reversion," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 314-318, May.
    7. Bolton, Patrick & Wang, Neng & Yang, Jinqiang, 2019. "Investment under uncertainty with financial constraints," Journal of Economic Theory, Elsevier, vol. 184(C).
    8. Michele Longo & Alessandra Mainini, 2015. "Learning and Portfolio Decisions for HARA Investors," Papers 1502.02968, arXiv.org.
    9. Delaney, Laura, 2021. "A model of investment under uncertainty with time to build, market incompleteness and risk aversion," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1155-1167.
    10. Chronopoulos, Michail & De Reyck, Bert & Siddiqui, Afzal, 2014. "Duopolistic competition under risk aversion and uncertainty," European Journal of Operational Research, Elsevier, vol. 236(2), pages 643-656.
    11. Luo, Yulei & Nie, Jun & Wang, Haijun, 2022. "Ignorance, pervasive uncertainty, and household finance," Journal of Economic Theory, Elsevier, vol. 199(C).
    12. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    13. Hui Chen & Jianjun Miao & Neng Wang, 2010. "Entrepreneurial Finance and Nondiversifiable Risk," The Review of Financial Studies, Society for Financial Studies, vol. 23(12), pages 4348-4388, December.
    14. Bolton, Patrick & Li, Ye & Wang, Neng & Yang, Jinqiang, 2020. "Dynamic Banking and the Value of Deposits," Working Paper Series 2020-13, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    15. Henderson, Vicky & Hobson, David, 2007. "Horizon-unbiased utility functions," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1621-1641, November.
    16. Wang, Huamao & Yang, Zhaojun & Zhang, Hai, 2015. "Entrepreneurial finance with equity-for-guarantee swap and idiosyncratic risk," European Journal of Operational Research, Elsevier, vol. 241(3), pages 863-871.
    17. Alain Bensoussan & Benoit Chevalier-Roignant & Alejandro Rivera, 2021. "Does Performance-Sensitive Debt mitigate Debt Overhang?," Post-Print hal-03364891, HAL.
    18. Alexander, Carol & Chen, Xi & Ward, Charles, 2021. "Risk-adjusted valuation for real option decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 1046-1064.
    19. Schachter, J.A. & Mancarella, P., 2016. "A critical review of Real Options thinking for valuing investment flexibility in Smart Grids and low carbon energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 261-271.
    20. Shibata, Takashi, 2008. "The impacts of uncertainties in a real options model under incomplete information," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1368-1379, June.

    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:eee:mateco:v:51:y:2014:i:c:p:1-11. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.