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Efficient hedging in general Black-Scholes model

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  • Kyong-Hui Kim
  • Myong-Guk Sin

Abstract

An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes model with constant drift and volatility coefficients. In this paper we considered the efficient hedging for European call option in general Black-Scholes model $dX_t=X_t(m(t)dt+\sigma (t)dw(t))$ with time-varying drift and volatility coefficients and in fractional Black-Scholes model $dX_t=X_t(\sigma B_H(t)+mdt)$ with constant coefficients.

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  • Kyong-Hui Kim & Myong-Guk Sin, 2013. "Efficient hedging in general Black-Scholes model," Papers 1308.6387, arXiv.org, revised Mar 2014.
    • Handle: RePEc:arx:papers:1308.6387
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    References listed on IDEAS

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    1. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xi-Li & Wang, Ying-Luo, 2010. "Pricing currency options in a fractional Brownian motion with jumps," Economic Modelling, Elsevier, vol. 27(5), pages 935-942, September.
    2. 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.
    3. 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.
    4. 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.
    5. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
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