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Conditional-Mean Hedging Under Transaction Costs in Gaussian Models

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  • Tommi Sottinen
  • Lauri Viitasaari

Abstract

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black-Scholes type pricing models where the Brownian motion is replaced with a more general regular invertible Gaussian Volterra process.

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  • Tommi Sottinen & Lauri Viitasaari, 2017. "Conditional-Mean Hedging Under Transaction Costs in Gaussian Models," Papers 1708.03242, arXiv.org.
    • Handle: RePEc:arx:papers:1708.03242
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    References listed on IDEAS

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    1. Wang, Xiao-Tian, 2010. "Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 438-444.
    2. Leland, Hayne E, 1985. "Option Pricing and Replication with Transactions Costs," Journal of Finance, American Finance Association, vol. 40(5), pages 1283-1301, December.
    3. repec:dau:papers:123456789/4654 is not listed on IDEAS
    4. Wang, Xiao-Tian & Zhu, En-Hui & Tang, Ming-Ming & Yan, Hai-Gang, 2010. "Scaling and long-range dependence in option pricing II: Pricing European option with transaction costs under the mixed Brownian–fractional Brownian model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 445-451.
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    7. Foad Shokrollahi & Tommi Sottinen, 2017. "Hedging in fractional Black-Scholes model with transaction costs," Papers 1706.01534, arXiv.org, revised Jul 2017.
    8. Emmanuel Denis & Yuri Kabanov, 2010. "Mean square error for the Leland–Lott hedging strategy: convex pay-offs," Finance and Stochastics, Springer, vol. 14(4), pages 625-667, December.
    9. Wang, Xiao-Tian, 2010. "Scaling and long range dependence in option pricing, IV: Pricing European options with transaction costs under the multifractional Black–Scholes model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 789-796.
    10. Wang, Xiao-Tian & Yan, Hai-Gang & Tang, Ming-Ming & Zhu, En-Hui, 2010. "Scaling and long-range dependence in option pricing III: A fractional version of the Merton model with transaction costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 452-458.
    11. Sottinen, Tommi & Viitasaari, Lauri, 2017. "Prediction law of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 155-166.
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