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Insiders' hedging in a jump diffusion model

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  • Kiseop Lee
  • Seongjoo Song

Abstract

In this paper, we formulate the optimal hedging problem when the underlying stock price has jumps, especially for insiders who have more information than the general public. The jumps in the underlying price process depend on another diffusion process, which models a sequence of firm-specific information. This diffusion process is observed only by insiders. Nevertheless, the market is incomplete to insiders as well as to the general public. We use the local risk minimization method to find an optimal hedging strategy for insiders. We also numerically compare the value of the insider's hedging portfolio with the value of an honest trader's hedging portfolio for a simulated sample path of a stock price.

Suggested Citation

  • Kiseop Lee & Seongjoo Song, 2007. "Insiders' hedging in a jump diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 537-545.
    • Handle: RePEc:taf:quantf:v:7:y:2007:i:5:p:537-545
    DOI: 10.1080/14697680601043191
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    References listed on IDEAS

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    1. José Corcuera & Peter Imkeller & Arturo Kohatsu-Higa & David Nualart, 2004. "Additional utility of insiders with imperfect dynamical information," Finance and Stochastics, Springer, vol. 8(3), pages 437-450, August.
    2. Rüdiger Frey, 2000. "Risk Minimization with Incomplete Information in a Model for High‐Frequency Data," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 215-225, April.
    3. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    4. Föllmer, Hans & Wu, Ching-Tang & Yor, Marc, 1999. "Canonical decomposition of linear transformations of two independent Brownian motions motivated by models of insider trading," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 137-164, November.
    5. David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413, October.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    2. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2016. "Numerical Analysis On Local Risk-Minimization For Exponential Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-27, March.
    3. Wei Wang & Linyi Qian & Wensheng Wang, 2016. "Hedging of contingent claims written on non traded assets under Markov-modulated models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(12), pages 3577-3595, June.
    4. Takuji Arai & Yuto Imai & Ryoichi Suzuki, 2015. "Numerical analysis on local risk-minimization forexponential L\'evy models," Papers 1506.03898, arXiv.org.
    5. Su, Xiaonan & Wang, Wensheng & Hwang, Kyo-Shin, 2012. "Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1777-1785.
    6. Behzad Alimoradian & Karim Barigou & Anne Eyraud-Loisel, 2022. "Derivatives under market impact: Disentangling cost and information," Working Papers hal-03668432, HAL.

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