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Static hedging and pricing American options

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  • Chung, San-Lin
  • Shih, Pai-Ta
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    Abstract

    This paper utilizes the static hedge portfolio (SHP) approach of Derman et al. [Derman, E., Ergener, D., Kani, I., 1995. Static options replication. Journal of Derivatives 2, 78-95] and Carr et al. [Carr, P., Ellis, K., Gupta, V., 1998. Static hedging of exotic options. Journal of Finance 53, 1165-1190] to price and hedge American options under the Black-Scholes (1973) model and the constant elasticity of variance (CEV) model of Cox [Cox, J., 1975. Notes on option pricing I: Constant elasticity of variance diffusion. Working Paper, Stanford University]. The static hedge portfolio of an American option is formulated by applying the value-matching and smooth-pasting conditions on the early exercise boundary. The results indicate that the numerical efficiency of our static hedge portfolio approach is comparable to some recent advanced numerical methods such as Broadie and Detemple [Broadie, M., Detemple, J., 1996. American option valuation: New bounds, approximations, and a comparison of existing methods. Review of Financial Studies 9, 1211-1250] binomial Black-Scholes method with Richardson extrapolation (BBSR). The accuracy of the SHP method for the calculation of deltas and gammas is especially notable. Moreover, when the stock price changes, the recalculation of the prices and hedge ratios of the American options under the SHP method is quick because there is no need to solve the static hedge portfolio again. Finally, our static hedging approach also provides an intuitive derivation of the early exercise boundary near expiration.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Banking & Finance.

    Volume (Year): 33 (2009)
    Issue (Month): 11 (November)
    Pages: 2140-2149

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    Handle: RePEc:eee:jbfina:v:33:y:2009:i:11:p:2140-2149

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    Web page: http://www.elsevier.com/locate/jbf

    Related research

    Keywords: American option pricing Early exercise boundary Static hedge Value-matching Smooth-pasting;

    References

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    Citations

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    Cited by:
    1. Wong, Hoi Ying & Guan, Peiqiu, 2011. "An FFT-network for Lévy option pricing," Journal of Banking & Finance, Elsevier, vol. 35(4), pages 988-999, April.
    2. Jun Cheng & Jin Zhang, 2012. "Analytical pricing of American options," Review of Derivatives Research, Springer, vol. 15(2), pages 157-192, July.
    3. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    4. Chung, Y. Peter & Johnson, Herb & Polimenis, Vassilis, 2011. "The critical stock price for the American put option," Finance Research Letters, Elsevier, vol. 8(1), pages 8-14, March.
    5. Chung, San-Lin & Shih, Pai-Ta & Tsai, Wei-Che, 2013. "Static hedging and pricing American knock-in put options," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 191-205.

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