Valuation of American Continuous-Installment Options
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
References listed on IDEAS
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- S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
- 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.
- Peter Carr & Robert Jarrow & Ravi Myneni, 2008.
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in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103
World Scientific Publishing Co. Pte. Ltd..
- Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
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