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Analytics for geometric average trigger reset options

Author

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  • Tian-Shyr Dai
  • Yuh-Yuan Fang
  • Yuh-Dauh Lyuu

Abstract

The geometric average trigger reset option resets the strike price based on the geometric average of the underlying asset's prices over a monitoring window. Similar contracts have been traded on exchanges in Asia. This paper derives an analytic formula for pricing this option with multiple monitoring windows. The analytic formula in fact is a corollary of a general formula that holds for a large class of path-dependent options: It prices any option whose value can be written as a linear combination of [image omitted], where X is a multinormal random vector and b is some constant vector. Numerical experiments suggest that the pricing formula approximates the values of arithmetic average trigger reset options accurately. Thus pricing the arithmetic average trigger reset option can benefit from using this formula as the control variate in Monte Carlo simulation. Numerical results also suggest that the geometric average trigger reset option does not have significant delta jump as the standard reset option, and this useful property reduces the hedging risk dramatically.

Suggested Citation

  • Tian-Shyr Dai & Yuh-Yuan Fang & Yuh-Dauh Lyuu, 2005. "Analytics for geometric average trigger reset options," Applied Economics Letters, Taylor & Francis Journals, vol. 12(13), pages 835-840.
    • Handle: RePEc:taf:apeclt:v:12:y:2005:i:13:p:835-840
    DOI: 10.1080/1350485052000345500
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    References listed on IDEAS

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    1. P. Forsyth & K. Vetzal & R. Zvan, 2002. "Convergence of numerical methods for valuing path-dependent options using interpolation," Review of Derivatives Research, Springer, vol. 5(3), pages 273-314, October.
    2. Chuang-Chang Chang & San-Lin Chung & Mark Shackleton, 2004. "Pricing options with American-style average reset features," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 292-300.
    3. R. C. Heynen & H. M. Kat, 1995. "Lookback options with discrete and partial monitoring of the underlying price," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(4), pages 273-284.
    4. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
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    Cited by:

    1. Guangming Xue & Bin Qin & Guohe Deng, 2018. "Valuation on an Outside-Reset Option with Multiple Resettable Levels and Dates," Complexity, Hindawi, vol. 2018, pages 1-13, April.

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