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Valuation of American Continuous-Installment Options

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  • Pierangelo Ciurlia
  • Ilir Roko

Abstract

In an American continuous-installment option the premium, instead of being paid up-front, is paid at a certain rate per unit time. At any time at or before maturity date, the holder has the right to terminate payments and either exercise the option or "walk away" from deal. Under the standard Black-Scholes assumptions, we can construct an instantaneous riskless dynamic hedging portfolio and derive a Partial Differential Equation (PDE) for the value of this option. This key result enables us to derive valuation formulas for American continuous-installment options using the well-known integral representation along the early exercise boundary. The finite difference approach to solve the PDE is also examined, and numerical techniques to implement the valuation formulas are presented

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 345.

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Date of creation: 11 Aug 2004
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Handle: RePEc:sce:scecf4:345

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Keywords: Option pricing; Hedging;

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  1. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
  2. Carl Chiarella & Adam Kucera & Andrew Ziogas, 2004. "A Survey of the Integral Representation of American Option Prices," Research Paper Series 118, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
  4. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
  5. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 541-552, November.
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