IDEAS home Printed from https://ideas.repec.org/a/bla/jbfnac/v30y2003i3-4p413-440.html
   My bibliography  Save this article

An Aggregation Theorem for the Valuation of Equity Under Linear Information Dynamics

Author

Listed:
  • David Ashton
  • Terry Cooke
  • Mark Tippett

Abstract

We state an Aggregation Theorem which shows that the recursion value of equity is functionally proportional to its adaptation value. Since the recursion value of equity is equal to its book value plus the expected present value of its abnormal earnings, it follows that the adaptation value of equity can normally be determined by a process of simple quadrature. We demonstrate the application of the Aggregation Theorem using two stochastic processes. The first uses the linear information dynamics of the Ohlson (1995) model. The second uses linear information dynamics based on the Cox, Ingersoll and Ross (1985)‘square root’ process. Both these processes lead to closed form expressions for the adaptation and overall market value of equity. There are, however, many other processes which are compatible with the Aggregation Theorem. These all show that the market value of equity will be a highly convex function of its recursion value. The empirical evidence we report for UK companies largely supports the convexity hypothesis.

Suggested Citation

  • David Ashton & Terry Cooke & Mark Tippett, 2003. "An Aggregation Theorem for the Valuation of Equity Under Linear Information Dynamics," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(3‐4), pages 413-440, April.
  • Handle: RePEc:bla:jbfnac:v:30:y:2003:i:3-4:p:413-440
    DOI: 10.1111/1468-5957.00003
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1468-5957.00003
    Download Restriction: no

    File URL: https://libkey.io/10.1111/1468-5957.00003?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
    ---><---

    References listed on IDEAS

    as
    1. Mark Tippett & Teresa Warnock, 1997. "The Garman‐Ohlson Structural System," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(7‐8), pages 1075-1099, September.
    2. David J. Ashton, 1997. ""Discussion of" The Garman-Ohlson Structural System," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(7&8), pages 1101-1110.
    3. Mark Tippett & Teresa Warnock, 1997. "The Garman-Ohlson Structural System," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(7&8), pages 1075-1099.
    4. Pope, PF & Walker, M, 1999. "International differences in the timeliness, conservatism, and classification of earnings," Journal of Accounting Research, Wiley Blackwell, vol. 37, pages 53-87.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. P. Weetman & E. A. E. Jones & C. A. Adams & S. J. Gray, 1998. "Profit Measurement and UK Accounting Standards: A Case of Increasing Disharmony in Relation to US GAAP and IASs," Accounting and Business Research, Taylor & Francis Journals, vol. 28(3), pages 189-208, March.
    7. David J. Ashton, 1997. "Discussion of The Garman‐Ohlson Structural System," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(7‐8), pages 1101-1110, September.
    8. Nelson, Karen K. & Barth, Mary E. & Cram, Donald, 2001. "Accruals and the Prediction of Future Cash Flows," Research Papers 1594r, Stanford University, Graduate School of Business.
    9. Stephen H. Penman, 1998. "Combining Earnings and Book Value in Equity Valuation," Contemporary Accounting Research, John Wiley & Sons, vol. 15(3), pages 291-324, September.
    10. Feltham, GA & Ohlson, JA, 1996. "Uncertainty resolution and the theory of depreciation measurement," Journal of Accounting Research, Wiley Blackwell, vol. 34(2), pages 209-234.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    12. Merton H. Miller, 1994. "Is American Corporate Governance Fatally Flawed?," Journal of Applied Corporate Finance, Morgan Stanley, vol. 6(4), pages 32-39, January.
    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. Denise A. Jones, 2018. "Using real options theory to explain patterns in the valuation of research and development expenditures," Review of Quantitative Finance and Accounting, Springer, vol. 51(3), pages 575-593, October.
    2. Beattie, Vivien, 2005. "Moving the financial accounting research front forward: the UK contribution," The British Accounting Review, Elsevier, vol. 37(1), pages 85-114.
    3. Juana Aledo Martínez & Juan Manuel García Lara & María T. González Pérez & Christos A. Grambovas, 2020. "An empirical assessment of proposed solutions for resolving scale problems in value relevance accounting research," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 60(4), pages 3905-3933, December.
    4. David Ashton & Terry Cooke & Mark Tippett & Pengguo Wang, 2004. "Linear information dynamics, aggregation, dividends and ‘dirty surplus’ accounting," Accounting and Business Research, Taylor & Francis Journals, vol. 34(4), pages 277-299.
    5. Mark Aleksanyan & Khondkar Karim, 2013. "Searching for value relevance of book value and earnings: a case of premium versus discount firms," Review of Quantitative Finance and Accounting, Springer, vol. 41(3), pages 489-511, October.
    6. Adam Ostaszewski, 2004. "‘Equity smirks’ and embedded options: the shape of a firm's value function," Accounting and Business Research, Taylor & Francis Journals, vol. 34(4), pages 301-321.
    7. Arturo Leccadito & Stefania Veltri, 2015. "A regime switching Ohlson model," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(5), pages 2015-2035, September.
    8. Victoria L. Hodgson & Allan Hodgson, 2008. "Marketing Communication Expenditures and Financial Capital—The Impact of Marketing as an Option," Australian Journal of Management, Australian School of Business, vol. 33(2), pages 333-353, December.

    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. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
    2. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    3. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    4. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    5. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    6. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    7. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    8. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.
    9. José Valentim Machado Vicente & Jaqueline Terra Moura Marins, 2019. "A Volatility Smile-Based Uncertainty Index," Working Papers Series 502, Central Bank of Brazil, Research Department.
    10. Jobst, Andreas A., 2014. "Measuring systemic risk-adjusted liquidity (SRL)—A model approach," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 270-287.
    11. Ciprian Necula & Gabriel Drimus & Walter Farkas, 2019. "A general closed form option pricing formula," Review of Derivatives Research, Springer, vol. 22(1), pages 1-40, April.
    12. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    13. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    14. Semih Yon & Cafer Erhan Bozdag, 2014. "Test of Log-Normal Process with Importance Sampling for Options Pricing," Proceedings of Economics and Finance Conferences 0401571, International Institute of Social and Economic Sciences.
    15. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.
    16. Peter Christoffersen & Ruslan Goyenko & Kris Jacobs & Mehdi Karoui, 2018. "Illiquidity Premia in the Equity Options Market," The Review of Financial Studies, Society for Financial Studies, vol. 31(3), pages 811-851.
    17. Shuang Xiao & Guo Li & Yunjing Jia, 2017. "Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-23, February.
    18. Ibáñez, Alfredo, 2008. "Factorization of European and American option prices under complete and incomplete markets," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 311-325, February.
    19. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    20. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.

    More about this item

    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:bla:jbfnac:v:30:y:2003:i:3-4:p:413-440. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0306-686X .

    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.