Finite Maturity Caps and Floors on Continuous Flows

20 Pages Posted: 22 Mar 2002 Last revised: 9 Mar 2008

See all articles by Mark B. Shackleton

Mark B. Shackleton

Lancaster University - Department of Accounting and Finance

Rafal M. Wojakowski

University of Surrey; Lancaster University - Management School


Models of interest rate caps and floors are typically based on discrete rates over finite horizons while existing real option models describe perpetual claims on the maximum of two continuous flows. In this paper we produce formulae for finite maturity caps and floors that are contingent on continuous flows. We present hedge ratios and discuss applications where a lognormally distributed flow variable is suitable. For other situations where practitioners use proprietary models, the formula presented is useful as a quick, tractable and universal means for mapping quoted implieds to prices and vice versa.

Keywords: Finite maturity, caps and floors, continuous flows, time integral of options, implied volatilities

JEL Classification: G12, G13

Suggested Citation

Shackleton, Mark B. and Wojakowski, Rafal M., Finite Maturity Caps and Floors on Continuous Flows. Journal of Economic Dynamics and Control, Vol. 31, No. 12, pp. 3843-3859, 2007, Available at SSRN: or

Mark B. Shackleton (Contact Author)

Lancaster University - Department of Accounting and Finance ( email )

The Management School
Lancaster LA1 4YX
United Kingdom
44 1524 594131 (Phone)
44 1524 847321 (Fax)

Rafal M. Wojakowski

University of Surrey ( email )

Faculty of Business, Economics and Law
The Surrey Business School
Guildford, Surrey GU2 7XH
United Kingdom
+44 1483 683477 (Phone)


Lancaster University - Management School ( email )

Lancaster, LA1 4YX
United Kingdom
+44 (1524) 593630 (Phone)
(01524) 847321 (Fax)


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