A Modified 'Square Root' Process for Determining the Value of the Option to (Dis)Invest

34 Pages Posted: 29 Nov 2004

See all articles by Paul J. M. Klumpes

Paul J. M. Klumpes

Nottingham Trent University

Mark J. Tippett

Loughborough University - Business School; University of Exeter Business School


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

Klumpes, Paul J.M. and Tippett, Mark J., A Modified 'Square Root' Process for Determining the Value of the Option to (Dis)Invest. Journal of Business Finance & Accounting, Vol. 31, No. 9-10, pp. 1449-1481, November 2004. Available at SSRN: https://ssrn.com/abstract=618310

Paul J.M. Klumpes

Nottingham Trent University ( email )

Burton Street
Nottingham NG1 4BU, NG1 4LN
United Kingdom

Mark J. Tippett (Contact Author)

Loughborough University - Business School ( email )

Ashby Road
Nottingham NG1 4BU, LE11 3TU
Great Britain

University of Exeter Business School ( email )

Streatham Court
Xfi Building, Rennes Dr.
Exeter, EX4 4JH
United Kingdom

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