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On the relationship of the dynamic programming approach and the contingent claim approach to asset valuation

Author

Listed:
  • Mihail Zervos

    (Department of Statistics, School of Mathematics and Statistics, University of Newcastle, Newcastle-upon-Tyne NE1 7RU, UK Manuscript)

  • Bernhard Meister

    (Goldman Sachs, ARK Mori Bldg., 5F, 12-32, Akasaka 1-chome, Minato-ku, Tokyo 107, Japan)

  • Thomas S. Knudsen

    (Bankers Trust, 1 Appold Street, Broadgate, London EC2A 2HE, UK)

Abstract

We consider a general model for an investment producing a single commodity, and, assuming that there exists a traded asset spanning the corresponding market, we prove a "verification theorem" which relates the solution of an appropriate differential equation with the investment's contingent claim price. In this way, we show in a mathematically rigorous way that the contingent claim approach and the dynamic programming approach to the problem of asset valuation are equivalent, modulo parameter calibration. Our analysis can be used in a straightforward way to address a big number of investment models.

Suggested Citation

  • Mihail Zervos & Bernhard Meister & Thomas S. Knudsen, 1999. "On the relationship of the dynamic programming approach and the contingent claim approach to asset valuation," Finance and Stochastics, Springer, vol. 3(4), pages 433-449.
    • Handle: RePEc:spr:finsto:v:3:y:1999:i:4:p:433-449
    Note: received: October 1997; final version received: September 1998
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    Citations

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    Cited by:

    1. Ewald, Christian Oliver & Taub, Bart, 2022. "Real options, risk aversion and markets: A corporate finance perspective," Journal of Corporate Finance, Elsevier, vol. 72(C).
    2. Caren Sureth, 2002. "Partially Irreversible Investment Decisions and Taxation under Uncertainty: A Real Option Approach," German Economic Review, Verein für Socialpolitik, vol. 3(2), pages 185-221, May.
    3. Rainer Niemann & Caren Sureth, 2002. "Taxation under Uncertainty – Problems of Dynamic Programming and Contingent Claims Analysis in Real Option Theory," CESifo Working Paper Series 709, CESifo.
    4. Niemann Rainer & Sureth Caren, 2005. "Capital Budgeting with Taxes under Uncertainty and Irreversibility / Investitionsplanung mit Steuern bei Unsicherheit und Irreversibilität," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 225(1), pages 77-95, February.
    5. Insley, M.C. & Wirjanto, T.S., 2010. "Contrasting two approaches in real options valuation: Contingent claims versus dynamic programming," Journal of Forest Economics, Elsevier, vol. 16(2), pages 157-176, April.
    6. Richard R. Lumley & Mihail Zervos, 2001. "A Model for Investments in the Natural Resource Industry with Switching Costs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 637-653, November.
    7. Gunther Friedl & Björn Anton, 2010. "Anforderungen an ein wertorientiertes Management Accounting in Banken," Schmalenbach Journal of Business Research, Springer, vol. 62(61), pages 83-107, January.

    More about this item

    Keywords

    Dynamic programming; contingent claims; non-arbitrage; real assets;
    All these keywords.

    JEL classification:

    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

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