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Improved method for static replication under the CEV model

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  • Tsai, Wei-Che

Abstract

This paper studies the hedging performance of static replication approach proposed by Derman, Ergener, and Kani (DEK, 1995) for continuous barrier options under the constant elasticity of variance (CEV) model of Cox (1975) and Cox and Ross (1976), and then focuses on how to improve the DEK method. Given the time-varying volatility feature of the CEV model, I show that the DEK static hedging portfolio exhibits serious mismatches of the theta values on the barrier, particularly when one of the component options of the portfolio is around the neighborhood of expiration, which primarily explains why static portfolio values are greater than zero on the barrier except at the matching points. The DEK method (hereafter, the improved DEK method) is improved by re-forming a static replication portfolio consisting of plain vanilla options and cash-or-nothing binary options with different maturities to match both the value-matching condition and the theta-matching condition on the barrier. The numerical analyses indicate that under the CEV model, the improved DEK method significantly reduces replication errors for an up-and-out call option.

Suggested Citation

  • Tsai, Wei-Che, 2014. "Improved method for static replication under the CEV model," Finance Research Letters, Elsevier, vol. 11(3), pages 194-202.
    • Handle: RePEc:eee:finlet:v:11:y:2014:i:3:p:194-202
    DOI: 10.1016/j.frl.2014.04.004
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Jia‐Hau Guo & Lung‐Fu Chang, 2020. "Repeated Richardson extrapolation and static hedging of barrier options under the CEV model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 974-988, June.
    2. Lee, Hangsuck & Ko, Bangwon & Lee, Minha, 2023. "The pricing and static hedging of multi-step double barrier options," Finance Research Letters, Elsevier, vol. 55(PA).
    3. Gurdal Ertek & Aysha Al-Kaabi & Aktham Issa Maghyereh, 2022. "Analytical Modeling and Empirical Analysis of Binary Options Strategies," Future Internet, MDPI, vol. 14(7), pages 1-23, July.

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    More about this item

    Keywords

    CEV; Static hedging; Binary option;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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