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A Modified ‘Square Root’ Process for Determining the Value of the Option to (Dis)invest

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  • Paul Klumpes
  • Mark Tippett

Abstract

We determine optimal investment criteria for a capital project whose cash flows evolve in terms of a ‘modified square root’ process. The modified square root process has properties similar to the Cox, Ingersoll and Ross (1985)‘square root’ process but in addition, encompasses the possibility of negative cash flows. Although closed form solutions for the valuation equations implied by the modified square root process are the exception rather than the rule we are able to show that analytic solutions, in the form of infinite power series expansions, will always exist. Furthermore, we also show that when a prescribed set of regularity conditions is satisfied, these power series expansions converge to closed form valuation functions. The optimality criteria for capital investment decisions are then simplified considerably.

Suggested Citation

  • Paul Klumpes & Mark Tippett, 2004. "A Modified ‘Square Root’ Process for Determining the Value of the Option to (Dis)invest," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(9‐10), pages 1449-1481, November.
    • Handle: RePEc:bla:jbfnac:v:31:y:2004:i:9-10:p:1449-1481
    DOI: 10.1111/j.0306-686X.2004.00580.x
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    References listed on IDEAS

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    1. Black, Fischer, 1995. "Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    2. Miles, David, 1993. "Testing for Short Termisn in the UK Stock Market," Economic Journal, Royal Economic Society, vol. 103(421), pages 1379-1396, November.
    3. 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.
    4. Huw Rhys & Mark Tippet, 2001. "A Binomial Basis for the Cox, Ingersoll and Ross Model of the Term Structure of Interest Rates," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(3‐4), pages 379-405, April.
    5. Huw Rhys & Mark Tippet, 2001. "A Binomial Basis for the Cox, Ingersoll and Ross Model of the Term Structure of Interest Rates," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 28(3-4), pages 379-405.
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