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Static hedging and pricing American knock-in put options

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  • Chung, San-Lin
  • Shih, Pai-Ta
  • Tsai, Wei-Che
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    Abstract

    This paper extends the static hedging portfolio (SHP) approach of Derman et al. (1995) and Carr et al. (1998) to price and hedge American knock-in put options under the Black–Scholes model and the constant elasticity of variance (CEV) model. We use standard European calls (puts) to construct the SHPs for American up-and-in (down-and-in) puts. We also use theta-matching condition to improve the performance of the SHP approach. Numerical results indicate that the hedging effectiveness of a bi-monthly SHP is far less risky than that of a delta-hedging portfolio with daily rebalance. The numerical accuracy of the proposed method is comparable to the trinomial tree methods of Ritchken (1995) and Boyle and Tian (1999). Furthermore, the recalculation time (the term is explained in Section 1) of the option prices is much easier and quicker than the tree method when the stock price and/or time to maturity are changed.

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    Bibliographic Info

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

    Volume (Year): 37 (2013)
    Issue (Month): 1 ()
    Pages: 191-205

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    Handle: RePEc:eee:jbfina:v:37:y:2013:i:1:p:191-205

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

    Related research

    Keywords: American knock-in options; Static hedging portfolio; Theta-matching condition; CEV model; Hedging effectiveness;

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    1. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    2. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
    3. Stephen Figlewski & Bin Gao, 1998. "The Adaptive Mesh Model: A New Approach to Efficient Option Pricing," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-032, New York University, Leonard N. Stern School of Business-.
    4. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    5. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    6. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06.
    7. Marti G. Subrahmanyam & Bin Gao & Jing-zhi Huang, 1998. "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-067, New York University, Leonard N. Stern School of Business-.
    8. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
    9. M. H. A. Davis & W. Schachermayer & R. G. Tompkins, 2001. "Pricing, no-arbitrage bounds and robust hedging of instalment options," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 597-610.
    10. Johannes Siven & Rolf Poulsen, 2009. "Auto-static for the people: risk-minimizing hedges of barrier options," Review of Derivatives Research, Springer, vol. 12(3), pages 193-211, October.
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