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A model‐free approximation for barrier options in a general stochastic volatility framework

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  • Frido Rolloos
  • Kenichiro Shiraya

Abstract

For a general stochastic volatility framework with correlation between the spot price and the instantaneous volatility, an analytical approximation for single barrier options with continuous monitoring is given. The approximation is expressed only in terms of market observable implied volatilities and prices. As such the approximation is independent of the specific form and number of parameters of the skew‐generating stochastic volatility model.

Suggested Citation

  • Frido Rolloos & Kenichiro Shiraya, 2024. "A model‐free approximation for barrier options in a general stochastic volatility framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(6), pages 923-935, June.
    • Handle: RePEc:wly:jfutmk:v:44:y:2024:i:6:p:923-935
    DOI: 10.1002/fut.22498
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    References listed on IDEAS

    as
    1. Hideharu Funahashi & Tomohide Higuchi, 2018. "An analytical approximation for single barrier options under stochastic volatility models," Annals of Operations Research, Springer, vol. 266(1), pages 129-157, July.
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    3. Jason Fink, 2003. "An examination of the effectiveness of static hedging in the presence of stochastic volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(9), pages 859-890, September.
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    5. Kenichiro Shiraya, 2020. "An Approximation Method For Pricing Continuous Barrier Options Under Multi-Asset Local Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(08), pages 1-20, December.
    6. Ali Hirsa & Georges Courtadon & Dilip B. Madan, 2003. "The Effect of Model Risk on the Valuation of Barrier Options," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 4(2), pages 47-55, January.
    7. Marc Romano & Nizar Touzi, 1997. "Contingent Claims and Market Completeness in a Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 399-412, October.
    8. Yukihiro Tsuzuki, 2014. "Pricing Bounds on Barrier Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1170-1184, December.
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    11. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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