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Valuation of American Continuous-Installment Options

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  • Pierangelo Ciurlia

    ()

  • Ilir Roko

    ()

Abstract

We present three approaches to value American continuous-installment options written on assets without dividends or with continuous dividend yield. In an American continuous-installment option, the premium is paid continuously instead of up-front. At or before maturity, the holder may terminate payments by either exercising the option or stopping the option contract. Under the usual assumptions, we are able to construct an instantaneous riskless dynamic hedging portfolio and derive an inhomogeneous Black–Scholes partial differential equation for the initial value of this option. This key result allows us to derive valuation formulas for American continuous-installment options using the integral representation method and consequently to obtain closed-form formulas by approximating the optimal stopping and exercise boundaries as multipiece exponential functions. This process is compared to the finite difference method to solve the inhomogeneous Black–Scholes PDE and a Monte Carlo approach. Copyright Springer Science + Business Media, Inc. 2005

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File URL: http://hdl.handle.net/10.1007/s10614-005-6279-4
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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 25 (2005)
Issue (Month): 1 (February)
Pages: 143-165

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Handle: RePEc:kap:compec:v:25:y:2005:i:1:p:143-165

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Web page: http://www.springerlink.com/link.asp?id=100248
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Keywords: installment option; free boundary-value problem; integral representation method;

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  1. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 1(2), pages 1-14.
  2. Carl Chiarella & Adam Kucera & Andrew Ziogas, 2004. "A Survey of the Integral Representation of American Option Prices," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 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, Wiley Blackwell, vol. 2(2), pages 87-106.
  4. 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.
  5. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
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