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Static hedging and pricing American knock-in put options

Author

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

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jbfina:v:37:y:2013:i:1:p:191-205
    DOI: 10.1016/j.jbankfin.2012.08.019
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    References listed on IDEAS

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    1. 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.
    2. San-Lin Chung & Pai-Ta Shih, 2007. "Generalized Cox-Ross-Rubinstein Binomial Models," Management Science, INFORMS, vol. 53(3), pages 508-520, March.
    3. 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.
    4. Espen Gaarder Haug, 2001. "Closed Form Valuation Of American Barrier Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 355-359.
    5. San‐Lin Chung & Pai‐Ta Shih & Wei‐Che Tsai, 2010. "A modified static hedging method for continuous barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(12), pages 1150-1166, December.
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    7. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
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    10. 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.
    11. 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.
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    Cited by:

    1. San‐Lin Chung & Yi‐Ta Huang & Pai‐Ta Shih & Jr‐Yan Wang, 2019. "Semistatic hedging and pricing American floating strike lookback options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 418-434, April.
    2. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2015. "Pricing and static hedging of American-style knock-in options on defaultable stocks," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 343-360.
    3. Ballestra, Luca Vincenzo & Cecere, Liliana, 2015. "Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley," Finance Research Letters, Elsevier, vol. 14(C), pages 45-55.
    4. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    5. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    6. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2020. "Early exercise boundaries for American-style knock-out options," European Journal of Operational Research, Elsevier, vol. 285(2), pages 753-766.
    7. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.

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    More about this item

    Keywords

    American knock-in options; Static hedging portfolio; Theta-matching condition; CEV model; Hedging effectiveness;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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